Talk:Monty Hall problem

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Changes suggested by JeffJor, Martin Hogbin, and Glkanter

If you're here because you've been invited to comment, there are ,two,. three (related) suggestions.

• #Glkanter's suggestion: Eliminate all 'host behaviour, etc' influenced discussion, save for the Wikipedia minimum necessary references to Morgan and his ilk, as the 'conditional' problem is the converse of "Suppose you are on a game show."

If nobody minds, I'd like to revise my proposal to make it more reflective of the literature: 3 Sections to the article: The unconditional MHP, A brief discussion on why Morgan and the 'conditional variants' are not the MHP, and 'diversions' - which includes 'variants', etc.

• #JeffJor's suggestion: The so-called conditional problem needs to be a separate article, with "conditional" in its title.

• #Martin Hogbin's suggestion: This article should concentrate on the unconditional solution with the Morgan's conditional solution in a variations section.

Please indicate in subsections below whether you favor or oppose each of these suggested changes.

The intent is to try to determine whether there is community consensus for any of these changes. I would suggest one subsection per user who is commenting, and to avoid endless arguments, restricting your comments to your own section (this is modeled after the process used at Wikipedia:Arbitration Committee). I've precreated sections for everyone I've explicitly invited to comment. -- Rick Block (talk) 15:31, 2 December 2009 (UTC)

Discussion about setting up this section and inviting folks to comment

In this section please summarize the changes you're suggesting. I'll be asking the set of folks I mentioned to Glkanter above to come here and offer their opinions, so please keep it as brief as possible. Please let me know when you think this section is ready for others to comment on. -- Rick Block (talk) 01:07, 1 December 2009 (UTC)

Rick, have you invited Boris Tsirel, William Connolley, or C S to contribute their opinions? What sort of time frame do you have in mind before 'In essence, silence implies consent' as per Wikipedia policy? Glkanter (talk) 15:47, 2 December 2009 (UTC)

I haven't invited anyone yet. The list of folks is the set of users I added below, plus I'll post something at Wikipedia:WikiProject Mathematics. I can specifically invite Boris, William, and C S if you'd like. As far as the timeframe, I was thinking maybe something like a week or two. -- Rick Block (talk) 15:53, 2 December 2009 (UTC)

I posted on Boris' page earlier this morning. Otherwise, don't do anything 'special' on my account. It just looked like you had sent out 'request for comments' by the way you set things up. Glkanter (talk) 16:02, 2 December 2009 (UTC)

I was going to, but had an edit conflict with Martin as he added his new section below. We need to straighten this out first. -- Rick Block (talk) 16:06, 2 December 2009 (UTC)

Yes, please include the 3 editors I mentioned. Thank you. Glkanter (talk) 16:11, 2 December 2009 (UTC)

kmhkmh was active for a while, too... Glkanter (talk) 16:54, 2 December 2009 (UTC)

Gill110951 perhaps? Glkanter (talk) 17:09, 2 December 2009 (UTC)

And Friday as well. Glkanter (talk) 17:27, 2 December 2009 (UTC)

I've notified all (including Wikipedia:WikiProject Mathematics) using template:please see referring them to this section. -- Rick Block (talk) 04:20, 3 December 2009 (UTC)

Glkanter's suggestion

This is from the section above.

Each instance in the article (and the various FAQs) of a host behaviour, or host bias, or host prejudice is indicative of a reliance on Morgan's paper. Regardless of what is being illustrated, this topic only exists among Morgan and a few others.

Since the problem statement of both vos Savant (Whitaker) and Krauss & Wang begins with: "Suppose you are on a game show", we know that this host behaviour will not be shared with the contestant, whose State of Knowledge is the only one asked for in The Monty Hall problem.

So, while Morgan is published, his argument is irretrievably flawed. The moment the problem is restated to rely on a host behaviour, it's no longer the Monty Hall problem. The problem statement becomes: 'Suppose you are not on a game show'. Which is the exact opposite of how both Monty Hall problem statements in the article begin: "Suppose you are on a game show". Morgan's criticism and his solutions are not relevant to the Monty Hall game show problem, which is the subject of this article.

Only because it's been published, Morgan should be referenced, but with such an obviously erroneous argument, it hardly deserves the great emphasis it currently enjoys. All other references to host behavior, etc., 'conditional vs unconditional', 'variants', and the Popular solutions being in any way inadequate should be removed from the article.

A second section would explain why Morgan and 'conditional variants' are not the Monty Hall problem

A final section on 'diversions' would include 'variants' and whatever else.

JeffJor's suggestion

Rick, I've changed my mind on one thing. The so-called conditional problem needs to be a separate article, with "conditional" in its title. It can be linked to the MHP, but it is not the MHP. For justification, see (and cite in the article) [url=http://www.jstor.org/stable/187880] Maya Bar-Hillel's article "How to Solve Probability Teasers," Philosophy of Science, Vol. 56, No. 2 (Jun., 1989), pp. 348-358. That addresses several points critical to the problem, that are quite specific to all of the arguments we have had here, incuding documented evidence. Specifically: (1) It's just a puzzle. It isn't supposed to present a rigorously-defined mathematical problem, (2) The simple assumptions implied by the informal problem statement are intended, and almost universally accepted by anyone who isn't expecting such a rigorously-defined mathematical problem, (3) Even when presented with alternate wordings that explicitly include elements of host strategy, the general audience does not take that strategy into account in their solutions, and (4) the clear majority of respondents get the wrong answer (1/2) that is based on naive intuition rather than a formal solution.

By separating the articles this way, Wikipedia can clearly present both problems in a fair and uncluttered manner, allowing any reader who wants to depend on the more formal approach to do so, and allowing those who do not see that formalism as necessary to limit themselves to the information that is of interest to them. JeffJor (talk) 15:03, 1 December 2009 (UTC)

Martin Hogbin's suggestion

We should take the current K & W statement as our starting definition of the MHP.

I suggest that we give the Whitaker statement first then say that the K & W statement is how this is generally interpreted. The K & W paper itself supports this view.

The primary solution and explanation should not use conditional probability

Although it can be argued that, even in the case where the host is defined to choose a legal door randomly, conditional probability should still be used because the action of choosing a particular door reduces the sample set and thus the opening of a specific door represents a conditioning of the sample set, it is clear that this is a trivial condition that it is not necessary to consider. This is quite evident either from the symmetry of the problem or from the fact that the revealing of random information tells us nothing. I am sure that we can find reliable sources to support this view.

The Morgan paper clearly does not answer the question as stated in the article and thus should not be regarded as our ultimate reliable source.

The Morgan paper introduces a parameter q for something that is defined by the article problem statement to have only the value of 1/2. The Morgan paper thus answers a different problem (I suggest that we call it the Morgan scenario) from that posed in the article. In the Morgan scenario it is known that the host might have some preference for one of the legal goat doors.

The Morgan solution should be introduced in a later section of the article that deals with variations of the problem.

There are many variations of this problem and the Morgan Scenario is just one of many.

Colincbn's comments

(referring to JeffJor's suggestion)

Hear, hear!! Colincbn (talk) 15:09, 1 December 2009 (UTC)

(referring to Glkanter's suggestion)

I really don't know jack about probability and whatnot, but I still tend to agree with Glkanter's points. I came to this article through looking up various paradoxes and this was a really neat one that I got to try out in the real world (see simulation question above). As I understand it the "Monty Hall problem" states that the host chooses randomly, so any other discussion about host behavior should be limited to the "Variants" section under "Other host behaviors". Just my 2 cents, Colincbn (talk) 02:41, 1 December 2009 (UTC)

• Just to clarify, I think a mention of the Host behaviour/Conditional problem should be made in a subsection of this article, such as the Variants section, with a "main article" link (ie: {{main|MHP Conditional solution}} ) to a separate article that goes into Morgan's conditional problem in detail. I figure this will give the casual reader all the info he/she is looking for with an easy way to delve into the mathematics more deeply if they want. (also thanks to Rick for maintaining this section!) Colincbn (talk) 01:07, 3 December 2009 (UTC)

Martin Hogbin's comments

I agree that this article should concentrate on the simple and notable interpretation of the MHP, namely the version in which a conditional solution is an unnecessary complication. Morgan's academic problem could be a section of this article or could form a new one. Martin Hogbin (talk) 22:02, 1 December 2009 (UTC)

Glkanter's comments

By my count, that's 4 in favor of the proposed changes, and 0 against. I've been championing these changes since October, 2008, Martin prior to that, and countless other editors for about 5 years. When can we declare an end to the pointless filibustering, acknowledge a consensus, and move on? Rick, will you be offering your comments? Have you contacted the others? Glkanter (talk) 22:29, 1 December 2009 (UTC)

About Martin Hogbin's suggestion - :I agree 100% with your proposed changes. I would like to add my 2 cents to the rationale, however. Morgan is criticizing and solving something other than the Monty Hall game show problem in the article. The introduction of the contestant being aware of any 'host behaviour' when selecting from 2 remaining goats changes the Problem Statement of both vos Savant/Whitaker and Karauss & Wang from "Suppose you are on a game show" to the converse, "Suppose you are not on a game show". Individual contestants on game shows are never provided more information than the 'average' contestant will have. There can be no 'condition'. It's illogical. Glkanter (talk) 15:33, 2 December 2009 (UTC)

JeffJor's comments

[Repeated in part from comments below]

The point of separating the articles is not to eliminate any POVs. It is to emphasize them. To not let one facet of the MHP (simple solution w nonintuitive result) become overpowered by the other (good teaching tool for conditional probabilites). If we don't physically separate them, we need to more clearly divide the article. The first part should be about the classic (unconditional) MHP, as stated by MvS (not K&W), and listing the set of assumptions she has said (and 99.9% of readers agree) are implied: interchangable doors, and any kind bias becomes irrelevant because of interchangeable doors. Then a section about game protocals (part of what some call host stratgies) such as always opening a door or revealing a goat, WITHOUT mention of bias or conditional problems. This mostly exists. Finally, you can cite Gillman (not Morgan) as a reference that introduces the possibility that the conditional problem is intended, but matters only if there is a bias. Use the K&W statement here, not Gillman's misquote. Gillman is better than Morgan because it is clearer, includes placement bias, and does not launch into possibilities that we are never told how to use. I think this is pretty consistent with Martin's suggestion. JeffJor (talk) 17:44, 4 December 2009 (UTC)

Rick, no paper that uses q<>1/2 is addressing the K&W problem. They allow for it as a very specific variant of what they are addressing. But make no mistake: they are treating the problem statement we are supposed to be working with as the variant. That is wrong. There is nothing wrong with addressing their solutions as the variant, because it is a (more general) variation of what the article is supposed to be about. It isn't even a variant that is supposed to be used: no references use it, they just present it and say you don't need to use it. And I feel you have been just as much as stone wall on points relating to this as you accuse others of being. Meow. JeffJor (talk) 17:56, 4 December 2009 (UTC)

Rick, you keep treating the Morgan POV as though it is involiate. It is not. Morgan misquotes the MvS problem statement, and so their claim that "the conditional problem is intended" cannot be taken as a reliable interpretation of the MHP. It is just a possible interpretation. Any reference that derives from Morgan is similarly suspect. Gillman misquotes, too, but in different ways. Bar-Hillel's survey proves that few (she found none) readers think of the conditional problem. More references exist that ignore it completely, than that address it. Krauss and Wang admit what the mis-quoters do not - I'll repeat it since when I said it before, it was apparently in cat language before - "Semantically, Door 3 in the standard version is named merely as an example." Grinstead and Snell separate the problem in the exact same two ways I suggested (and in fact, were a model for the suggestion). In short, it is a very minor POV that the conditional problem is meant, and it is based on citable misquotation and misinterpretation. JeffJor (talk) 18:24, 4 December 2009 (UTC)

Rick Block's comments

As a matter of fundamental Wikipedia policy, articles MUST be written from a neutral point of view. What the proponents of these changes are essentially suggesting is that this article take the POV that the interpretation of the problem described by a significant number of reliable sources (the Morgan et al. reference and others) is invalid. Even if this were a stance taken by reliable sources (which, as far as I know, is not the case), by relegating the "Morgan" interpretation to a "variant" subsection or splitting it into a POV fork this article would then be taking the "anti-Morgan" POV. I've made this point to these editors numerous times before, but yet they keep tendentiously arguing that the "Morgan" POV is wrong, or the Morgan et al. reference has errors, or (most recently) that the Morgan POV is NOT about the "real" Monty Hall problem (as if by convincing me that their POV is "correct" I would then agree with the changes they're suggesting).

I sincerely hope the "consensus" from this process is against making these changes, because even if there is a consensus for these changes they cannot be implemented - doing so would violate Wikipedia policy. -- Rick Block (talk) 04:01, 3 December 2009 (UTC)

You all realize Martin's proposal implies the article will not even mention conditional probability except in a "variant" section, don't you? How anyone can think this is not a blatant POV issue escapes me. -- Rick Block (talk) 20:19, 3 December 2009 (UTC)

And why so dramatic, Rick? We've all disagreed with you on this forever. Glkanter (talk) 22:02, 3 December 2009 (UTC)

Yes Rick, all three proposals are consistent that way. It's based on this very recent and brief section of this talk page (following long and lengthy discussions on various 'talk' and 'argument' pages), 'Is The Contestant Aware?':

http://en.wikipedia.org/wiki/Talk:Monty_Hall_problem#Is_The_Contestant_Aware.3F

I started this section at 11:28, 29 November 2009 (UTC). You responded with 2 vague, filibuster-style questions, and at 23:02, 1 December 2009 (UTC) I wrote this:

"Rick, I have directly asked you this question many times, and have never seen a direct 'yes or no' answer from you. As this is a crucial element of the consensus that has been built, it is essential that we understand your reasons if you do not agree with the paragraph above:

"Has it been agreed by the editors of this article that regardless of how Monty handles the 'two goats remaining' situation, the contestant has no knowledge of the method?". [This question was ommitted when I asked Rick the 3rd time. I include it here for clarity]

""It seems to me that this is a (unstated) premise of the problem, as both vos Savant (Whitaker) and Krauss and Wang begin the problem statement with: 'Suppose you're on a game show'. I read this as clearly stating it is only the contestant's point of view we are concerned about. And, being a game show, the host is prohibited from divulging to the contestant either where the car is, or where the car is not.""

To date, at 20:36, 3 December 2009 (UTC), you have still not responded directly to this question. Glkanter (talk) 20:36, 3 December 2009 (UTC)

I have to state the opposite view, which is that you have taken a ridiculously pro-Morgan POV. There are many reliable sources that relate to the MHP and not all of them have a host door choice parameter. Those that do generally quote Morgan as the source for this.

The article already takes a problem statement from a reliable source (K & W) and that same source confirms that this is how most people view the problem. In that statement, the host is defined to choose a legal goat door randomly. It is thus a simple matter of fact that the Morgan paper does not address that problem in so far as it allows a door choice parameter where none is permitted by the problem statement.

The Morgan paper clearly addresses a scenario where where the player is somehow aware of the host's policy for choosing a legal goat door. This rather bizarre scenario is not the one described by our problem statement and thus it should be viewed as a variant of the MHP as it is most commonly understood. Martin Hogbin (talk) 21:30, 3 December 2009 (UTC)

I thought I made it clear we were to use arbcom style rules here, which are that you only comment in your own section (it really does help keep the threads from getting absurdly long). However, since you've been rude enough to post here I'll respond to each of you, BUT please do not continue this as a thread here.

Glkanter asks why so dramatic? The argument has shifted from "present an unconditional analysis first (and don't criticize it)" to "exclude the conditional analysis completely (except as a variant)". This is a huge difference.

Glkanter asks why I haven't responded about his "Is The Contestant Aware?" question. Why should I? Glkanter has repeatedly demonstrated a complete lack of comprehension of nearly everything I've ever said. It's like trying to explain something to a cat. At some point you just have to give up. However, I'll give it another go. Meow, meeeow, meow, meowww. I'm not sure I have that quite right since I don't speak cat, but it's probably about as comprehensible to him as anything else I could say.

Martin (incorrectly) claims again that the Morgan et al. paper does not address the K&W version of the problem. Quote from the paper: "Incidentally, Pr(W_s | D3) = 2/3 iff p = q = 1/2". This is the solution to the K&R version of the problem statement. The Morgan et al. paper (and the Gillman paper and many, many others who approach the problem conditionally) absolutely address the K&R version. Because they also address other versions doesn't mean they don't address the K&R version.

In the K & W statement q=1/2 by definition thus any problem in which q might not be equal to 1/2 must be a different problem. It is that simple. Martin Hogbin (talk) 19:04, 4 December 2009 (UTC)

Martin and Glkanter are both apparently completely incapable of understanding the main point of the Morgan et al. paper (and the Gillman paper, and what Grinstead and Snell have to say) which is that the MHP is fundamentally a conditional probability problem and that there's a difference between an unconditional and conditional solution. What these sources are saying is that a conditional solution clearly addresses the MHP (as they view the problem), but an unconditional solution doesn't unless it's accompanied by some argument for why it applies to the conditional case as well (and there are many valid arguments, but no argument at all which is what is generally provided with most unconditional solutions is not one of them). The fact that the problem can be (and typically is meant to be) defined in such a way that unconditional and conditional solutions have the same numeric answer in no way invalidates what these sources say. To have the article take the stance that the conditional solution is invalid (which would be truly absurd), or that the criticism these sources make of unconditional solutions is incorrect, or that a conditional solution applies only to a "variant" is making the article take a POV. This would be a direct violation of a FUNDAMENTAL Wikipedia policy. -- Rick Block (talk) 01:53, 4 December 2009 (UTC)

Glopk's comments

Delayed response (am not a very active editor at all these days), but here it is.
Statement

I support Rick Block's statement as expressed above, and am in favor of keeping the article more or less in the state in which it passed the last FA review, with minor edits where needed. I am in strong disagreement with all three suggestions above (JeffJor, Glkanter, Martin Hogbin). In particular, I am in strong support of keeping the language that differentiates between the conditional (Bayesian) interpretation of the problem and the unconditional (elementary) one.

Motivation. The purpose of an encyclopedia is to present a "best" selection from the body of knowledge about each topic, being POV neutral as well as reader-neutral. --glopk (talk) 18:53, 29 December 2009 (UTC)

Chardish's comments

Thanks for the invitation to comment. In my opinion, Martin Hogbin's suggestion seems the post prudent. The Monty Hall problem as popularly explained doesn't rely on conditional probability, and the Whitman explanation seems sufficient for anyone who is not a mathematician. Wikipedia is a general-purpose encyclopedia, and as such main articles should focus on explaining topics as they are popularly understood, with specific scientific analysis relegated to separate articles.

And, to be honest, the article as it stands is much harder to read and understand (as a layperson) than it was several years ago. NPOV isn't "pleasing everyone equally"; don't let efforts towards neutrality wind up hurting the article. - Chardish (talk) 02:53, 6 December 2009 (UTC)

Melchoir's comments

Just from reading the present Wikipedia article, I agree with Martin Hogbin's suggestion, because I don't see why allowing the host to prefer one goat over the other is a more relevant generalization than allowing the host other behaviors. Melchoir (talk) 06:47, 3 December 2009 (UTC)

Nijdam's comments

I fully support Rick's view. Nijdam (talk) 10:34, 3 December 2009 (UTC)

To make my position crystal clear: there is no such as an unconditional solution. There are different problems: an unconditional problem and a conditional one. The latter generally being called the MHP. Nijdam (talk) 22:24, 3 December 2009 (UTC)

Please read my proposal. I do not claim that the MHP is an unconditional problem. What I say is that in the problem definition given in the article the host is taken to choose a legal goat door randomly. Morgan address the case where this choice is non-random,thus they do not address the problem as defined in this article. Martin Hogbin (talk) 22:39, 3 December 2009 (UTC)

I'm in the audience looking at the stage. I see three doors and a player pointing to one of them. From the two remaining doors one is opened and shows a goat. That's what I call the MHP. (And I know of the random placement of the car and the random choice of the host.) Nijdam (talk) 22:50, 3 December 2009 (UTC)

Quite, and that is not the problem that the Morgan paper addresses. The Morgan paper addresses the case where the host door choice is not random. Thus the Morgan paper addresses a variation on what we all agree is the MHP. Martin Hogbin (talk) 23:28, 3 December 2009 (UTC)

Quite, but that is not the problem we are continuously arguing about. Even "our" MHP needs conditional probabilities. Nijdam (talk) 15:04, 4 December 2009 (UTC)

The problem that you and K & W describe, which is the problem addressed by this article, is one in which q=1/2 by definition. Therefore, any problem in which there is a possibility that q might not equal 1/2 must be a different problem. Morgan clearly consider a problem in which it is possible for q to have a value other than 1/2. The problem they consider therefore must be different from that in which q is defined to be 1/2. Morgan do indeed address a (bizarrely) more general problem than the one we are considering but it is, for sure, a different problem. Martin Hogbin (talk) 19:35, 4 December 2009 (UTC)

Dicklyon's comments

I haven't been watching this article for a while; glad to see the K&W treatment up front; that looks like the most sensible article I've seen on it. As for the Morgan conditional approach, I think it's an unnecessary distraction, but it's out there in mainstream reliable sources about the topic, so we ought to cover it in the article. I think Martin Hogbin's proposal sounds best. Dicklyon (talk) 05:01, 3 December 2009 (UTC)

I agree with Rick Block that the other two proposals essentially violate WP:NPOV; but I disagree that moving the conditional stuff to a more minor position is a problem; his heavy promotion of the conditional approach violates WP:UNDUE in my opinion. Dicklyon (talk) 16:29, 3 December 2009 (UTC)

Henning Makholm's comments

I have long since given up on following these discussions, and am not even a very active editor these days. However, since somebody went to the length of creating a heading for me, here are my general recommendations -- for whatever they are worth:

1. The article absolutely should discuss assumptions about the host's behavior. It is impossible to derive a valid answer without making some assumptions, and differences in which assumptions are implicit are one of the main reasons why smart people can disagree on the solution when the problem is stated sloppily. It would be a sorry encyclopedia that purported to treat the Monty Hall problem without explicitly pointing out this kind of confusion.
2. The analysis that involves conditional probabilities and the one that considers whole-game expectations under different player strategies are both valid ways of approaching the problem, each with its own advantages and disadvantages. The article should present both, and must not suggest that one of them is inherently better or more correct than the other. (For this reason I would oppose splitting one of the analyses into a separate article, suggesting that it solves a fundamentally different problem, rather than being an alternative way of approaching the same problem).
3. There has been far too much microlinguistic analysis about precise wordings of the problem in this source or that one, trying to argue that this analysis or that one is the one that most directly addresses the question being asked (implying that the other is a detour via a different but non-canonical presentation of the problem). Which analysis one chooses depends depends far more on which properties (besides being valid) one wants of it. For example, raw convincing power for a lay audience would favor the whole-game analysis, whereas a more in-depth discussion of the effect of different assumptions of the host's behavior is most easily done using conditional probabilities.
4. Editors should keep in mind that Wikipedia is an encyclopedia, not a textbook, an question-and-answer database, or a Court of Public Opinion. The goal of an encyclopedia article is not to answer one particular question but to present a body of knowledge. Therefore the amount of energy spent on negotiating "the" question that this article should be about answering is fundamentally misspent. The body of knowledge the article ought to present encompasses several different but related questions (some of which are sometimes mistaken for each other), and several different way of approaching some of them. An approach that restricts ourselves to discussing just one of them would fail to cover the topic encyclopedically.
5. I have no strong opinion about which analysis should be first in the article, as long as it is not being touted as inherently superior or inferior by virtue of its position. However, the general principle of progressing from the "quick and easily understood" to the "more complex but also more general and (possibly) enlightening" would seem to suggest starting with the whole-game analysis.

–Henning Makholm (talk) 07:13, 3 December 2009 (UTC)

Most people, including Rick, think that the problems should be addresses from the player's point of view (state of knowledge). As has been pointed out by many people, it is extremely unlikely that the player would have any knowledge of the host's door opening policy, thus from the player's point of view the host policy must be taken as random (within the rules).

I have no objection to the Morgan scenario (in which the payer is assumed to know the host's policy) as well as the more simple case being presented here provided that it is made clear exactly what case this applies to.

What you call, 'microlinguistic analysis about precise wordings of the problem' was started by Morgan et al. who added a pointless layer of obfuscation to a simple puzzle that most people get wrong.

The point is that the simple/symmetrical/non-conditional problem is the notable one and therefore it should come first. More complex versions should come later for the few that are interested in such complications. Martin Hogbin (talk) 22:36, 4 December 2009 (UTC)

Boris Tsirelson's comments

I summarize my position in two points:

• 1. The symmetric case is more important for an encyclopedia than the general case. (Likewise, a circle is more important for an encyclopedia than an arbitrary curve.)

• 2. The coexistence of the conditional and the unconditional can be more peaceful. (Not just "numeric coincidence" in the symmetric case; see #Not just words and #Formulas, not words.)

Boris Tsirelson (talk) 06:44, 9 December 2009 (UTC)

Being invited by Glkanter, I quote here some paragraphs of a discussion that happened on my talk page on February 2009. As far as I understand, my position is close to that of JeffJor. Boris Tsirelson (talk) 17:20, 2 December 2009 (UTC)

Why split? Because of different importance. The "conditional" article will be, say, of middle importance, while the "unconditional" article – of high importance. We surely have our point of view about importance (rather than content). Boris Tsirelson (talk) 05:54, 4 December 2009 (UTC)

The quotes follow.

Each time giving the course "Introduction to probability" for our first-year students (math+stat+cs) I spend 20-30 min on the Monty Hall paradox. I compare two cases: (a) the given case: the host knows what's behind the doors, and (b) the alternative case: he does not know, and it is his good luck that he opens a door which has a goat. Im addition I treat the case of 100 (rather than 3) doors (just like Monty Hall problem#Increasing the number of doors). And, I believe, students understand it.

I have no idea, why some people spend much more time on the Monty Hall paradox (and even publish papers). (Boris Tsirelson)

This simple little problem is deeper than it might appear, and likely well worth more than 20-30 mins of lecture time. Perhaps even worth revisiting once or twice during a term to explore its more subtle aspects. (Rick Block)

Deeper than it might appear? OK, why not; but still, for now I am not enthusiastic to deep into it. Tastes differ. I find it more instructive, to restrict myself to the simpler, symmetric case, and compare the two cases mentioned above.

If an article leaves many readers puzzled, why it is unnecessarily complicated, it is a drawback. (Boris Tsirelson)

If a problem that appears so simple to me, like the Monty Hall problem, is not sufficiently solved using my unconditional proof, in what circumstances is the unconditional proof appropriate? Thank you. (Glkanter)

The unconditional argument shows that "always switch" is better than "never switch". This is what it can do. Let me add: if you (that is, the player) are not informed about possible asymmetry then you cannot do better than these two strategies, either "always switch" or "never switch". (Boris Tsirelson)

Well, I gotta ask. Do you still prefer JeffJor's proposal among the 3 proposals put forth? Glkanter (talk) 07:19, 9 December 2009 (UTC)

Really, I have nothing to add to the two points that summarize my position (above). Any move toward them is good for me. My resolution power, and my acquaintance with the literature, are too low for choosing between different proposals; I leave this matter to more informed (and less lazy) editors. Boris Tsirelson (talk) 08:22, 9 December 2009 (UTC)

kmhkmh's comments

I'll start with a clear statement and give some more detailed information afterwards:

I strongly disagree with any of the 3 suggestions (JeffJor, Glkanter, Martin Hogbin) and aside from minor difference fully support Rick Block's approach

If one surveys the available literature literature/publications on the topic, you pretty much get an relatively obvious outline for the article: original problem (in vos savant's column), unconditional solution (basically vos savant and/or various math sources), conditional solution (Morgan and almost in any math source), various problem variation and caveats, history of the problem, application of the problem outside the math domain. Which is essentially for the most part, what we already had and what Rick managed to maintain. In that context I fully agree with Henning Makholm's comments above, who puts it fairly well. The article wouldn't have such problems if all participants would follow that rationale.

The fuzz over quality or minor mistakes in Morgan's paper is a somewhat ridiculous distraction, since Morgan's paper is not needed to argue the conditional solution or caveats to the unconditional solution at all. There is plenty of other math literature dealing with the problem in more or less the same manner.

My personal advice would be to pass the article for final thorough review and modification to the math or a science portal. During that review neither of the 4 disagreeing authors (JeffJor, Glkanter, Martin Hogbin, Rick Block) are allowed to participate/edit. After that review the article should be fully protected for good.

I've seen what happened to the German version, that had similar problems (without a Rick Block around to constantly remain some standard). So we had a lot of people with a somewhat fanatic approach constantly pushing for their favoured explanation and constantly ignoring wiki standards, common sense and more important the available literature on the subject. As result mathematicians and scientists basically dumped the article and gave up on improving it.An effect this article has partially seen as well.--Kmhkmh (talk) 16:45, 4 December 2009 (UTC)

Kmhkmh, no one is proposing a reduction in the quality of this article but you miss some essential points out in your outline. We should have: 'original problem (in vos savant's column), unambiguous problem definition (K&W), solution to the unambiguous problem (which is trivially conditional but need not be treated so, basically vos savant and/or various math sources), the Morgan scenario (in which the player knows host door choice policy) the conditional solution (Morgan). Martin Hogbin (talk) 19:46, 4 December 2009 (UTC)

I don't quite see how that is "missing" in my outline above nor do I see any particular reason to give (K&W) a preferred treatment, such an approach does not reflect the publications on the topic.--Kmhkmh (talk) 20:11, 4 December 2009 (UTC)

I am not proposing that we give K&W and preference but must have a clear and unambiguous problem statement before we (or anyone else) can attempt to answer the problem. Morgan do not have such a statement in their paper so we must use one from another reliable source, in this case another published paper. Note that the lack of clear problem statement in the Morgan paper is not just my opinion, that same point is made clear in the comment by Prof Seymann published in the same journal immediately after the Morgan paper. Martin Hogbin (talk) 20:20, 4 December 2009 (UTC)

I'm really not interested in repeating now here the discussion that you're pushing for almost over a year now and which frankly from my perspective is entirely pointless and misguided. The original problem in vos Savant's column was ambiguous and hence various articles on the topic and its variations provide their own specifications. As pointed out above already Morgan doesn't really matter in that regard. What the Wikipedia article has to do, is to describe the all various specification and not arbitrarily picking one like K&W as the "right" one. I'd recommend you to reread Henning Makholm's comments carefully. Or to put it rather bluntly - you asked for my comment here it is: Leave the article alone.--Kmhkmh (talk) 21:46, 4 December 2009 (UTC)

Actually I did not ask for your comment here and I certainly did not ask for, and do not need, your permission to edit Wikipedia. Neither did I pick K&W as the 'right one' as you put it, somebody else put it in the article as a clear and unambiguous description of the problem. As it happens I agree with whoever did this as K & W is the only published paper to seriously address the question of how most people interpret the MHP. It is therefore an excellent place to start the article. Martin Hogbin (talk) 22:25, 4 December 2009 (UTC)

Gill110951's comments

No comment right now. But a lot of Christmas break reading to do here, to catch up. Happy Wikipedia Christmas, everyone! Gill110951 (talk) 13:27, 20 December 2009 (UTC)

Summary of opinions

I have added names to the sections below based on comments above. If I have got it wrong please move yourself.
Please do not make comments in this section.
Editors are invited to sign against their names to confirm that they are in the right section. Martin Hogbin (talk) 11:29, 5 December 2009 (UTC)

Martin, What exactly do you mean by "for change" and "against change"? Dicklyon and JeffJor's opinions (for example) seem very different to me. By categorizing them both as "for change" I think you may be misrepresenting the situation. It would be better to be more specific about what change you're talking about, i.e. Glkanter's suggestion (remove any mention of conditional probability and any host behavior variants) Eliminate all 'host behaviour, etc' influenced discussion, save for the Wikipedia minimum necessary references to Morgan and his ilk, JeffJor's suggestion (separate articles - basically Glkanter's suggestion plus create a new article for the "conditional" treatment), your suggestion (I'm not exactly sure precisely how to summarize yours). In addition, rather than "against change" the other alternative should probably be described in terms of what it is for, which I think could be described as "present both unconditional and conditional solutions without taking a POV about the validity of either one". And, I'll note that for the article to say that Morgan et al. criticize the unconditional solutions is not the same as taking that POV. You do understand this difference, don't you? -- Rick Block (talk) 16:52, 5

Although there may be some discussion over the details it is fairly clear that several people would like to see the simple/unconditional solution/problem given more prominence here. This is the change that I am referring to. 'Against change' is fairly self explanatory Martin Hogbin (talk) 16:58, 5 December 2009 (UTC)

For change

Colincbn
Martin Hogbin Martin Hogbin (talk) 11:29, 5 December 2009 (UTC)
Glkanter Glkanter (talk) 12:16, 5 December 2009 (UTC)
JeffJor
Melchoir
Dicklyon
Boris Tsirelson Boris Tsirelson (talk) 15:27, 5 December 2009 (UTC)
Gill110951 (talk) 13:28, 20 December 2009 (UTC)

Against change

Rick Block
Nijdam
kmhkmh
Glopk

Unable to classify

Please move your name to the correct section if appropriate. Martin Hogbin (talk) 11:24, 5 December 2009 (UTC)
Henning Makholm
Chardish (I object to summary classification of my comments. - Chardish (talk) 00:59, 11 December 2009 (UTC))

The Mathematics Rule I Am Properly Applying

Way back in junior high, we did some proofs or problems or something to do with absolute values. That's all I can remember.

But the thing I do remember is that after you 'solved' the problem, you had to go back and check each of the results to make sure it didn't violate the original problem statement in some way.

That's all I'm saying about Morgan and the rest. When you check your work with some 'host behaviour' variant, it no longer meets the original problem statement, "Suppose you're on a game show..." Go ahead and argue. Better you should save your breath. Hosts don't tell contestants where the car is.

So, as an encyclopedia, Wikipedia will properly refer to reliably published sources like Morgan. And Devlin. No problem.

But, as a self-appointed 'explainer' of all things MHP, I think the article improperly gives the conditional solutions way too much emphasis. Because it doesn't match the original problem statement any longer. Glkanter (talk) 21:47, 6 December 2009 (UTC)

Often one solves a problem by saying something like "let x be the distance travelled". One converts the problem to algebra, and finds a solution "x=-2 or x=3". Lazy students quit there. But good students think. We go back and remember that we wanted a distance and it had to be positive, so the real answer is x=3. This is a fine problem solving strategy. One solves a relaxation of the problem, that is to say one solves the problem while forgetting about some of the constraints, finds some answers, and then looks to see if any satisfy the original problem. But I wouldn't call this strategy a "mathematics rule". I'm not sure it applies in this case, where the original problem is somewhat ambiguous. It turns out that there are a number of interesting MHPs. Gill110951 (talk) 05:19, 22 December 2009 (UTC)

What I'm saying is that the so-called 'variants' do not satisfy the original problem. As I see it, the contestant being aware of any host bias is mutually exclusive with 'Suppose you're on a game show'. That's why the question the 'opposed' editors refuse to answer, 'Is the Contestant Aware...' is so pivotal to these discussions. A game-breaker, really. Glkanter (talk) 05:32, 22 December 2009 (UTC)

The Meta Paradox of The Monty Hall Problem Paradox

Selvin poses the MHp. He solves it unconditionally at 2/3 vs 1/3 if you switch. The problem is hailed as a great paradox.

vos Savant prints a letter inspired by Selvin in a general interest USA Sunday newspaper supplement. She solves it unconditionally at 2/3 vs 1/3 both when you made your choice, and when the switch is offered. Because Monty's actions don't impart usable knowledge to the contestant. It's a sleight of hand. Nothing happened.

All heck breaks out. Tens of thousands of letters, including over 1,000 from PhDs tell her she's wrong. And they are certain!

vos Savant soothes the savage beasts with logic and smarts. The unconditional solution carries the day. The problem is, again, hailed as a great paradox.

This group, "J. P. Morgan, N. R. Chaganty, and M. J. Doviak are Associate Professors and R. C. Dahiya is Professor, all in the Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia" (284 The American Statistician, November 1991, Vol. 45, No. 4 (C 1991 American Statistical Association) develops the argument that the problem is only properly solved using a conditional problem statement. Their criticisms, etc. rest on this: That when faced with 2 goats, the host must decide which goat to reveal. This rests on the assumption (presumption, invention) that the contestant might somehow gain usable information as to the location of the car in this particular instance of the game by Monty's actions. It's left unstated whether Monty's actions would be shared with the contestant. And if they are shared, what method is used. But it's clear: in this instance of game play they claim, the subject contestant could be armed with more useful information that the average contestant.

The only problem is, their 'assumption' is not consistent with the first words of the MHP problem statement: "Suppose you're on a game show...", as Hosts don't tell contestants where the car is hidden. Actually, some Wikipedia editors have found a math error in the paper, and are in communication with the publication. Oh, and "Richard G. Seymann is Professor of Statistics and Business Administration, School of Business, Lynchburg College, Lynchburg, VA 24501" (1991 American Statistical Association The American Statistician, November 1991, Vol. 45, No. 4 287) wrote a paper that spoke only about Morgan's paper. It was included in the very same issue of the journal. It's weird. Is it a disclaimer, a clarifier? It's sure not an endorsement.

Others come out with papers supporting Morgans criticisms, including Gillman in 1992 and Grinstead and Snell 2006.

Others continue publishing unconditional papers. (It seems likely that if 3 Wikipedia editors plus Seymann find fault with the paper, so too would members of the Professional Mathematics Community. And as professionals, they don't make a big stink about it. They just ignore the paper and continue publishing articles that rely solely on the unconditional problem statement.)

So, has the Professional Mathematics Community decided that Morgan is right, and Selvin was a hack? I don't think so. Before, during and after Morgan's paper, respected, credentialed reliable Mathematics professionals continued to publish articles solving the MHP unconditionally. I don't know that any of these professionals in either camp have attacked or counter-attacked anyone else's paper. It looks to me, that in the Professional Mathematics Community nothing happened. No usable information was gained. Perhaps Morgan's paper, like Monty revealing a goat is just sleight of hand, imparting no usable knowledge? It's possible. Most published MHP articles say nothing of Morgan or conditionality.

Which brings us, finally, to the Meta Paradox. The Wikipedia editors are arguing, essentially, over whether or not solving the unconditional problem is 'enough'.

Suppose you are given a story problem about a game show. The Professional Mathematics Community agrees heartily that this is a delightful paradox which can be 'proved' or 'solved' using an unconditional problem statement. Maybe not even requiring formal probability notation. Symbolic notation is often used. Then "J. P. Morgan, N. R. Chaganty, and M. J. Doviak are Associate Professors and R. C. Dahiya is Professor, all in the Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia" come forth and say it must be solved conditionally, based on the arguments set forth in their paper. You are then offered to stay with the unconditional solution being complete, or you may switch to the conditional solution.

Many people are fooled by this paradox, and accept the switch. Because they don't realize that like Monty revealing the goat, no new usable information has been revealed by this paper. Nothing happened. Glkanter (talk) 18:27, 8 December 2009 (UTC)

I like this way of looking at things! Except that there is no law against studying conditional Monty Hall problems, and quiz-players should also realize what they get when they go with the unconditional solution. So I think that something useful did come of the Morgan et al. contribution. Now we just need a reputable mathematician to publish a peer reviewed paper on the Monty Hall paradox paradox, and then wikipedia editors can write articles on it. Gill110951 (talk) 05:36, 22 December 2009 (UTC)

Glad you like it, thanks! It's a free country. They can do what they want. It just adds no value to those simply wanting to understand the MHP paradox. As the article is written, quite the opposite! There's an old salesperson's saying, 'Don't close past the sale' (it may actually be 'Don't sell past the order'). I may have had a professor say something like, 'Don't over-solve the test problems. Solve it and move on'.

Maybe you could look at my 'Huckleberry' section and tell me how his approach was insufficient, and how his results would have been improved by someone explaining to him the 'equal goat door constraint'? Glkanter (talk) 05:48, 22 December 2009 (UTC)

OK, I'm Paraphrasing slightly...

When asked how he was able to sculpt the venerated 'David', Michelangelo replied, 'It was easy really. I removed everything that didn't look like David'.

A comment from a newcomer to this discussion

Wow, this thread is long! And I haven't even looked at the archive(s?). I thought it might be worthwhile to make a comment as a person who has not been following this thread before now. I just, in the last couple of days, read the article and a big portion of the discussion.

My comment is simple: Please, I am not attacking anyone; I am just making a general, honest, respectful IMO comment. (And yes, I am schooled in mathematics.) I agree with those that say the article is too long, very unwieldy, and often downright confusing. I think the article as it now stands is almost worthless. I agree with those who say: Just state the "standard" problem as most people assume it is stated, and give a simple explanation as to why it is correct. Then meander off into the conditional and unconditional ponderings, the Bayesian statistics, etc.

I started out reading the article, with expectation of fun. I was already familiar what the "Monty Hall problem", and I understood it, at least in its more obviously stated form (based on the generally accepted assumptions). As I read on I thought, "Whaaa???" Much of the -- sorry, but most -- of the article is a murky mess, and even those who are somewhat probabilistically astute I think would have difficulty making sense of some of it. I'll cite just one example: The section titled "Popular Solution" is, IMHO, poorly written and confusing. Frankly, it's not clear what the author is meaning to get across in several places (even though I understand exactly what it is that he/she is intending to say). It needs to be rewritten, as does much of the rest of the article. Not tweaked, but rewritten. This sort of muddled presentation is just not necessary, and it is not worthy of the standards of Wikipedia. This stuff is not string theory or Gödel's incompleteness theorems in ZFC. This is introductory-level probability, albeit a very subtly tricky example of it.

I never seen an article on Wikipedia that has created such a WikeWar as this article has. It apparently has no resolution in sight. Anyway, I'm all out of suggestions -- if I have even made any.

Finally, just for fun, I wanted to mention a somewhat similar conditional-probability problem which I haven't seen anyone else mention. (It is not relevant to this article, nor should it appear in it; it's just related.) You play a "flip three coins game". The person I am gambling with shakes up three fair coins in a canister and spills them onto the table top. I am not allowed to see the coins initially before I make my choice; the canister shaker (my opponent) hides the coins from me. The rules are, the shaker peeks at the coins on the table and he has to tell me what the "majority" coin is. There will be either a majority of heads (3 heads or 2 heads) or a majority of tails (3 tails or 2 tails). Then, having been told what the majority is, I must guess what the third coin is -- heads or tails. If I get it right I get paid a dollar by the shaker; if I get it wrong, I pay him two dollars. Most people would think this a stupid gamble on my part; they will assume that the guess as to the heads-tails of the third coin has a 50-50 chance of being right. But it's easy to see (though it is initially counter-intuitive to many people) that if you always guess the opposite of the majority, you will win 3/4 of the time. Just write down all combinations: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT, and it's obvious. That would make a cool bar game. Even offering your opponent the 2-to-1 payoff, you would still win, on average, in the long run 25 cents per play:

   1/4*(-2) + 3/4*(1) = 1/4 of a dollar per coin-shake, in the long-run average.

Good luck with your little war. Worldrimroamer (talk) 23:53, 8 December 2009 (UTC)

There's no war. Just good faith disagreement. Likely to end soon, anyways. Is there any reason this editor's comments should not be reflected in our quorum building? Glkanter (talk) 01:18, 9 December 2009 (UTC)

I'm afraid I don't understand what you mean. Who is the "this editor" to whom you refer? I tried to state at the outset that I was not targeting my comments at any particular person. I did not compile a ledger of who wrote what. I was just making general comments, in the hopes that they might be a small but helpful contribution. —Preceding unsigned comment added by Worldrimroamer (talk • contribs) 03:10, 9 December 2009 (UTC)

Er... the obvious guess is that the third coin is the same as the majority, which is a bloody good guess: it is correct 3/4 of the time, both conditionally on the majority being heads, and conditionally on the majority being tails, and unconditionally on the nature of the majority. I shall try this in the pub to see if my population is smarter than Worldrimroamer's. Gill110951 (talk) 05:45, 22 December 2009 (UTC)

Sorry for being so cryptic. 'The editor' is you. As we try to bring this discussion to a close, we are attempting to build a Wikipedia Consensus to make changes very much as you described. So, I was asking the other editors if there is any reason your opinion should not be considered as part of the 'let's change the article' consensus, of which I am a part. It's all good. I think you'll find the discussion of the last few weeks most meaningful. Some extra Wikipedia Mathematics Project people have begun contributing, by request, and it's helped move things forward a great deal. Again, sorry for being unclear. Glkanter (talk) 03:27, 9 December 2009 (UTC)

Glkanter, thanks for your reply. I understand now what you meant. And by referring to "editing wars" I did not mean to be denigrating. Perhaps I should have used a different term. I just thought it was very interesting that this "simple" little topic has stirred up so much discussion. It does my heart good to see that there are people that care about esoterica like this (at least, in the eyes of the general public it would seem like esoterica). Best regards to all ... Worldrimroamer (talk) 17:48, 9 December 2009 (UTC)

Worldrimroamer, thanks for you contribution. New thought is always welcome here. One thing I might explain is that the article as it is now (more or less) in not the end result of the pages of discussion that you have seen. It is little changed in principle from the original FA version.

There are basically two broad factions of editors here. Those who want to keep the article as it is (or perhaps as it was about a year ago) and those who want to change the article to reflect more or less what you say, namely that The Monty Hall Problem is a simple mathematical puzzle that most people get wrong. What the article needs (according to the pro-change editors) is an initial section that concentrates on a simple description of the puzzle with normal 'puzzle assumptions' (all choices are random unless specified etc). This should be followed by some simple, convincing solutions that show why the player has a 2/3 chance of winning by switching.

The anti-change editors believe that the proposed changes are not justified by the available sources and that making them would jeopardise the article's FA status. Of particular importance is a paper by Morgan et al. which claims that the problem must be treated as one of conditional probability. This has the effect of changing the simple problem that most people get wrong to a complicated problem that most people are bored by. I strongly dislike the Morgan paper, you should get a copy and see what you think.

It the moment, apart from a few minor changes, the article is still built around the Morgan paper. The editors who want change have refrained from drastic editing as fought to get a consensus for change here. So far although there is a majority for change there is far from general agreement.

There are some things that are generally agreed on such as the game rules (the host always offers the swap and always opens a unchosen door to reveal a goat) the fact that overall the player has a 2/3 chance of winning by switching, and that it is assumed that the player has not studied replays of old shows to gain statistical information. I might add that, although there are strong opinions on both sides discussion has generally remained civil and there has been no edit warring. Martin Hogbin (talk) 11:57, 9 December 2009 (UTC)

Thanks, Martin. Yes, I understand what you mean about the basic disagreement. It sounds like a rather intractable situation to me. I hope you guys can work something out. As I told Glkanter in the post immediately above, I should perhaps not have used the term "edit wars". I just meant that it was impressive how much intense interest has been evidenced in this discussion. I think that's a good thing. I just wish that the article were not so ... opaque? IMO, Wikipedia should be accessible both to the experts in the field, as well as to the (curious and smart) not-so-expert people. There's room for both. I'll butt out now and wish you luck. You may need it. :o) Best regards. Worldrimroamer (talk) 17:48, 9 December 2009 (UTC)

__________________________________________________ —Preceding unsigned comment added by Worldrimroamer (talk • contribs) 17:51, 9 December 2009 (UTC)

The links are at the top of this talk page - as of the last FARC the article looked like this. Since then the "Solution" section (that arguably took the POV that the "unconditional" solution does not address the question as asked) has been split into a "popular solution" and "probabilistic solution" in a more NPOV manner. Saying this is "relatively unchanged" understates the situation fairly dramatically. What this extended discussion is about is furthering this change, to make the article effectively take the POV that a "conditional solution" is an unnecessary nuisance - i.e. that the POV presented by the aforementioned Morgan et al. paper is invalid. Saying the article in its current form, or even as of the last FARC is "built around the Morgan paper" is (IMO) factually false.

No article is ever finished and improvements are always welcome. This extended discussion is about whether additional changes are necessary to undo the POV some editors think was present in the version at the last FARC. -- Rick Block (talk) 15:35, 9 December 2009 (UTC)

Repeated text

Why does the entire Krauss and Wang text appear twice in the first bit of the article? Isn't the article long enough without this repetition? RomaC (talk) 14:48, 10 December 2009 (UTC)

Please see WP:Lead section. The lead is meant to be a concise, standalone overview of the entire article. The K&W problem definition was added to make the problem description unambiguous (even in the lead). I would be fine with deleting it and presenting only the Parade description. I predict others will object to this. -- Rick Block (talk) 15:44, 10 December 2009 (UTC)

Actually I kind of like the FARC lead better, it clearly states that the problem as stated in Parade is ambiguous. The K&W problem is in the beginning of the Problem section as an example of an unambiguous way of stating the problem anyway so I don't think it is entirely necessary in the lead. But I would rather work on consensus of the other suggested changes above before diving into those waters... Colincbn (talk) 16:10, 10 December 2009 (UTC)

Now I'm curious. Has Selvin's original statement been considered for the article? I've never read it. vos Savant made the MHP famous, but Selvin made it. Glkanter (talk) 16:16, 10 December 2009 (UTC)

Oohh, that might be a great idea. It would prevent repeating both the vS and K&W versions. of course there would also need to be a bit of rewording to make sure the information about the Parade article can stay in the lead and still make sense... Colincbn (talk) 16:27, 10 December 2009 (UTC)

Unlike the Parade statement of the problem, Selvin's statement is not very well known. It's also considerably longer. Because Jstor makes the first page of any reference available as a preview, it can be viewed online here. -- Rick Block (talk) 17:39, 10 December 2009 (UTC)

I like the solution though. Selvin's answer is published in a reliable source and I would like to see it in the article (but in the form of a pretty diagram). It treats the opening of either of the two unchosen boxes by the host as equivalent. Martin Hogbin (talk) 22:28, 10 December 2009 (UTC)

Isn't it funny how we've argued so much about vos Savant's failings and intents with the problem statement, and we never, since I've been around, discussed Selvin, et al's. I'm going to go read that page right now! I guess collaboration really can work. Who knew? Rick, thank you very much for the link! Glkanter (talk) 22:37, 10 December 2009 (UTC)

It says it all - it gives a simple solution (showing that the contestant has a 1/3 chance of winning if they stick and a 2/3 chance if they swap) and notes that the contestant's chance of having the car in their original box is unchanged at 1/3 after Monty has opened a door. Not only that but it was published in the same peer-reviewed journal as Morgan but it is not followed by a highly critical comment. Looks like a winner to me. Martin Hogbin (talk) 23:43, 10 December 2009 (UTC)

From a sourcing perspective, it is important to note that this is a letter to the editor, not an article. Articles from peer reviewed journals are usually the most reliable sources. Letters to the editor are more like primary sources. -- Rick Block (talk) 17:18, 11 December 2009 (UTC)

You might also be interested in Selvin's second letter in vol 29 #3. I can't find a pdf of the journal page online, but there's what appears to be a faithful copy here. Although I haven't compared it to the copy I have of the printed journal page, it's clearly missing a "/" on the 4th line of the conditional probability expansion. BTW - references to both of these have been in the article for several years. -- Rick Block (talk) 05:35, 11 December 2009 (UTC)

Thanks for that. It does not, in my opinion, discount the solution given the his original letter. The interesting point, when you look at that history of the problem, is that Monty actually never offered the swap and, if Selvin's account is accurate, it was the contestant who suggested it. Martin Hogbin (talk) 09:56, 11 December 2009 (UTC)

The other point which becomes apparent is that Monty, who was the only person who knew for sure his door opening policy, has clearly stated that he knew the contestants chance of holding the car remained at 1/3 after he had opened his door. That seems to me to rule out Morgan's conjecture that he might have had a preference for one door or the other. Martin Hogbin (talk) 09:56, 11 December 2009 (UTC)

Thanks, Rick, for finding a solution that resolves my concern (an overly long intro) Butwhatdoiknow (talk) 00:02, 21 December 2009 (UTC)

What has to be considered the MHP??

I very much like this question to be answered first. (BTW several sources mention the MHP to be equivalent to the three prisoners problem.) Nijdam (talk) 22:35, 15 December 2009 (UTC)

I created a "construction" site, where we may step by step build the article, until we come at a point we don't find agreement on. —Preceding unsigned comment added by Nijdam (talk • contribs) 16:41, 16 December 2009 (UTC)

Nijdam, have you joined the consensus? Is mediation still necessary? What conclusions did you and Boris reach? Please address my points from this diff Huckleberry & Awareness and these questions before we invest all the time and effort. Glkanter (talk) 16:51, 16 December 2009 (UTC)

I think everyone would like an answer to that question but it is unlikely that there will be agreement on the subject. I would say that there are several formulations of the problem. I would personally like the MHP be treated initially as a mathematical puzzle, formulated in such a way as to make the solution simple and not depend on conditional probability. In my opinion the MHP is fundamentally a simple problem that most people get wrong, this is undoubtedly its most notable aspect. This was obviously Gardner's intention with the TPP although you might still argue that this problem is still, strictly speaking, conditional. The difficulty with implementing my preferred approach here is that there are no sources that specifically treat the problem in that way, unless we can find one.

Without doubt, the most notable problem statement is Whitaker's but, as you are well aware, this leaves so much unsaid that it can be interpreted in many different ways. In my opinion vos Savant answered the question correctly (but failed to make clear exactly what the question was) whilst Morgan interpreted the question too strictly (and still ambiguously) and then answered their interpretation (for the most part) correctly.

The only unambiguous problem formulation that I know of in the literature is the Krauss and Wang version that we quote. This is exactly equivalent to the TPP but this suffers the problem that, although the effect of conditionality is negated by the host's random choice, it can still be argued (as you do) that the problem is still strictly one of conditional probability and thus, unfortunately, it is not amenable to a simple solution.

So, I regret that I have failed to answer your very important question. The lack of an answer is the cause of much of the argument here. I think we just have to argue it out as best we can to create the best article possible. Martin Hogbin (talk) 11:00, 16 December 2009 (UTC)

Here is the Monty Hall problem:

"Suppose you're on a game show..."

The symmetry is a premise. And needs no disclaimer or footnoting. Anybody that disagrees should tell me what's wrong with Huckleberry's approach and must answer, incorrectly, that 'the contestant is aware' to Is The Contestant Aware? Glkanter (talk) 11:22, 16 December 2009 (UTC)

From Wikipedia's perspective, the MHP is whatever reliable sources say it is. WE don't need to (in fact, we don't get to) decide. What we do need to do is say what reliable sources say about whatever they consider it to be.

As I thought I made clear above, reliable sources do not answer the question of what exactly is the MHP. We have at least Selvin's original statement, Whitaker's question, vos Savant's partial formulation, Morgans misiquotation and subsequent incomplete formulation, and several formulations in K&W. The only one that is unambiguous is the one we quote from K&W, but K&W make no claim that this is The MHP. Thus reliable sources do not answer the question and we must decide what the subject of our own article is to be here.

Martin - you keep saying it's a simple problem that most people get wrong and that approaching it as a conditional probability problem is (more or less) a nuisance. If it's so simple, why (in your opinion) do most people get it wrong? My answer to this is that they try to solve it conditionally (what was it in the K&W experiment - 35 out of 36 subjects consider only the case where the player has picked Door 1 and the host has opened Door 3), which means to me that we can't fully explain it without addressing this issue.

Yes we can, there is no evidence anywhere that anyone considers it important which door the host opens. K&W's main point is that giving door numbers just confuses the issue, and I agree. Martin Hogbin (talk) 18:14, 16 December 2009 (UTC)

Regardless of the above, since reliable sources address it both ways the article must also. Not to do so would imply a POV that the "unconditional" approach is better or more correct. Avoiding this POV is the reason I'm suggesting we go back to a single Solution section. JeffJor seems to be OK with this (since he's engaged in editing a proposal for such a suggestion). I can't tell if Glkanter is OK with this or not. You (Martin) are at least currently saying you're not OK with this (is that right?). So, directly, would both of you (Nijdam, too) be OK with a single solution section more or less like JeffJor's suggestion? -- Rick Block (talk) 15:04, 16 December 2009 (UTC)

Rick, I didn't realize I hadn't made my position clear. The 'Solution section' will contain simple solutions only. No disclaimers, no footnotes, no 'buts'. This is what the consensus has agreed to. Your NPOV threats are just that. They are intimidation, and an attempt at prior restraint. Just more filibustering, as usual. And Rick, nobody is buying your NPOV act. The current article has such a heavy Rick Block/Morgan bias it's laughable. The FAQs alone make me want to vomit. Just getting to NPOV from your extremes will be an accomplishment. I can't conceive of the article ever being so POV-ed in the other direction as great as you have accomplished. I agree, as you posted on the Mediation Cabal page, this discussion is totally out of control. How many times does the consensus have to tell you your interpretations are inconsistent with the consensus? Glkanter (talk) 15:20, 16 December 2009 (UTC)

Whoa, whoa, whoa. Rick, you have a sad way of imnposing your own POV in every possible way that lets you keep it in the article. It is downright insulting. I am not "OK" with considering the Morgan "conditional" approach as addressing the MHP. It does not. Seymann says it does not. Nobody, not even Morgan, says it does address the actual question. But I am a realist, and I recognize that you will not let it be separated AS IT SHOULD BE, because you feel justified in your POV because your misread those sources and think they say something they do not.

So I am "OK" with trying to improve the article in a way that can be accomplished. That means inculding your un-intended, not-MHP, POV in the article. Specific door numbers were never intended to be important, and any possible importance implied by the "reliablle sources" you quote, who demonstratably misrpresented the MHP, was for rigor only. It gets removed by those sources before actually addressing the MHP with their formula. IT HAS NOTHING TO DO WITH THE MHP. IT IS NOT REPRESENTATIVE OF THE MHP. IT DOES NOT HELP IN UNDERSTANDING WHY THE MHP IS CONTROVERSIAL. All it does is extend the thought problem, in a way that is interesting only to mathematicians. The body of the article needs to address the problem as seen by the general populace, not pedantic mathematicians who proved one assumption (of two similar ones that are normally made) was unnecessary. While interesting, being unnecessary doesn't explain the unintuitive nature of the problem. JeffJor (talk) 22:46, 16 December 2009 (UTC)

It seems like we must not be talking about the same thing here. I'm talking about a conditional probability analysis, like the one you wrote above (the paragraph starting "Another way to analyze the problem ..."). Which I think is exactly the way the general populace, not pedantic mathematicians, see the problem. What are you talking about? -- Rick Block (talk) 23:07, 16 December 2009 (UTC)

Rick, this is exactly why you and Nijdam cannot be the self appointed 'lead editors' for the consensus in favor of the change proposals. You do not understand the paradox in the same way as the consensus does. Glkanter (talk) 23:25, 16 December 2009 (UTC)

Hear! Hear! Glkanter (talk) 22:53, 16 December 2009 (UTC)

Except for the 'giving in to Rick and Nijadm' to the detriment of the honesty of the article part. Glkanter (talk) 22:58, 16 December 2009 (UTC)

Jeff - if you can reply I would appreciate it. My assumption was that since you wrote the above paragraph that you would be OK with putting it (or something like it) in the article. If that was not your intent I'm sorry to have misinterpreted. -- Rick Block (talk) 01:53, 17 December 2009 (UTC)

Rick - Just to be clear, there are four categories that different sources have used to approach the MHP. I will call them "Unconditional Approach," "Symmetric Conditional Approach," "Asymmetric Conditional Approach," and "Reduced Asymmetric Conditional Approach." UA, SCA, ACA, and RACA for short. And there can be different kinds of RACAs, depending on what gets "reduced," by which I mean eliminating the importance of a condition.

The UA supports either MvS's explanation, or Devlin's combined doors, or anything similar. It really doesn't utilize the doors in any specific way. It can be done rigorously (G&S do it in their first solution not attributed to MvS), but usually isn't. Non-rigorous solvers use symmetry to reduce G&S's twelve cases to four. The SCA looks at specific doors, but assumes that any uncertainty must be uniformly assigned as in G&S's second solution. Some UAs - those that mention door numbers - look like SCAs but are really using numbers only as examples. The "tree" version as it currently exists did this. You can tell because it has four cases that sum to P=1, not twelve cases as in G&S. ACA is stated in K&W (not Morgan, Gillman, or G&S since all ignore car placement bias) as Equation 1. But it is not useable to answer the question "Should she switch?" because of the placement bias. Morgan, Gillman, and G&S use an RACA where they make one reduction - they eliminate placement bias by assumption. K&W discuss several ways of reducing ACA by assumption - their no/one/two door solutions. Morgan's thesis is not that ACA is proper (although they mistakenly assume it), but that you don't need to assume anything to reduce the importance of host choice. They reduce it by making it unimportant to the quesiton, and that is still a reduction. Eventually, every source that considers an ACA reduces it to a question (not a probability value) that is answered independent of door numbers.

So, what I think is that UA needs to be the primary focus of the article. SCA can be used, or not; but if you insist on it, it needs to be done properly as G&S did. That's why I changed the probabilities in the discussion I wrote of it. I don't think you will let anybody take it out of the body completely, so I left it and did my best to improve it. But it really does not help non-students of probability. They don't understand that conditional probability depends as much on what is removed as what is left. The terms in the SCA formula can show this, but the non-student will not understand how to read such a formula. So it really doesn't help them, it just makes the article look like a textbook that they don't want to read. And any ACA is addressing a variant of the MHP where asymetric probabilites need to be considered. Few people think the problem says that, and fewer still think they can be used. Certainly not any of the references, who always reduce ACA completely. So I don't see any benefit from that to the general public. There is benefit to students of probability, but that benefit is not directly related to the MHP itself. It only shows how you don't have to make assumptiosn to reduce all of the conditiosn that might affect a strategy. So it can be included AS LONG AS IT IS CLEARLY SEPARATED FROM THE ACTUAL MHP DISCUSSION. And it needs to be made clear that it is a non-standard interpretation of the problem, and that the parts that make it diffewrent are never used directly to answer the MHP.

I hope this helps you and Nijdam. It is the ACA and RACA that belong as a variant. The SCA is "better" solution in the sense of rigor only; but it does not satisfy any need the article has, except rigor. Since the reason the MHP is enigmatic at all has nothing to do with rigor, but with intuition, we really should pay more attention to the issues that surround intuition. JeffJor (talk) 15:35, 17 December 2009 (UTC)

I don't need help. What you call UA, suggesting an approach to the MHP, is just a solution of a specific simple version, not the K&W-formulation, and in my opinion also lacking the characteristics of the MHP. This is also admitted by G&S: This very simple analysis, though correct, does not quite solve the problem that Craig posed. The SCA and ACA are both solutions to the MHP (K&W version). Nijdam (talk) 12:55, 20 December 2009 (UTC)

(1) Nijdam, elsewhere you had asked for my interpretation. When I "hoped it helped" you, I meant "helped you understand my interpretation." (2) But you apparently do need my help, because you think something other than UA/SCA is "the MHP." As has been clearly demonstrated through references,UA/SCA is indeed what was intended as "the MHP" by the originators, whether or not some others misinterpreted it. And all of the controversy in the general public surrounding those puplications stem directly from, and only from, it. Anything else is a distraction. The fact that some sources disagree on this point only proves that we need to handle that disagreement by separating the issues. Craig's problem can solved, as written. This is clearly admitted by Seymann. It is G&S's alternate interpretation that cannot be solved. They only supply a solution to an isolated example that they do not claim is as a valid solution the problem itself. And in fact, G&S is the model for how to do this. They separate their approaches the exact same way. JeffJor (talk) 13:04, 21 December 2009 (UTC)

You know what, JeffJor? Formulate in correct terminology what you consider to be a possible version of the MHP and add an appropriate solution. Nijdam (talk) 14:07, 21 December 2009 (UTC)

Nobody can solve the problem that Craig posed because it is not clear exactly what it is. Morgan interpreted it in one particular way that makes the problem clearly conditional. In fact he probably just wanted to know, 'What is the probability you win if your strategy is to switch?', as Morgan put it. Martin Hogbin (talk) 15:32, 20 December 2009 (UTC)

Incorrect, Martin. Read Seymann's comment to Morgan. It was not supposed to be a rigorous prob=l;em statement, it was a "fun" puzzle in a newspaper. And there are clear assumptions that can, and should, be made; which were reinforced by MvS herself. The controversy had nothing to do with any of those possible ambiguities. JeffJor (talk) 20:55, 20 December 2009 (UTC)

Jeff it would probably help our cause if you were to stop jumping down my throat at the first opportunity. I was the first, I believe, to bring to the attention of editors here Seymann's commentary, which points out that the problem can be interpreted in different ways. I am agreeing with you that Whitaker probably just wanted the simple unconditional problem answered, with normal 'puzzle' assumptions (as correctly made by vos Savant). That is why I quoted from Morgan's example of an unconditional statement of the problem. Even that 'most reliable of sources' gives the problem to which the simple solutions, including vos Savants are the answer; that is what I have quoted from. Martin Hogbin (talk) 21:23, 20 December 2009 (UTC)

It would help if we were all on the same page. Any ambiguity in the Parade statement is unimportant to what makes the MHP controversial. Considering such is what leads some people to think the Morgan analysis should be part of the main issue. The point is, that the Whitiker statement is sufficient for the vehicle in which it was published. Seymann does not say it "can be interpreted in different ways." He says, and I quote, "Simply put, and quite clear considering her suggestions for simulation procedures in her two later columns, the host is to be viewed as nothing more than an agent of chance who always opens a losing door, reveals a goat, and offers the contestant the opportunity to switch to the remaining, unselected door." There is nothing vague about this. Craig's problem can be solved, without having to allow for any alternate host strategies.

Rick (and others) keeps trying to inject his POV by suggesting Seymann thought it was ambiguous, and Seymann did not. And MvS said explicitly that the vast majority of the controversy in the letters had nothing to do with such possibilities. Your comment came in the middle of an "edit battle" where Rick reworded the article to inject that POV, and I removed it. As long as they keep trying, NPOV requires it be squelched. It is only this way that we can eliminate POV from the article. JeffJor (talk) 23:11, 20 December 2009 (UTC)

I will leave you to your lone battle as you seem determined to pick fights with those who essentially agree with you. I was arguing that Craig's question should be treated in a manner sympathetic to its origin long ago. Martin Hogbin (talk) 00:12, 21 December 2009 (UTC)

I'll note that I didn't "reword" anything. Butwhatdoiknow's complaint was the length of the lead. There was a pending suggestion on the talk page to drop the K&W problem statement in favor of the Parade problem statement. He dropped the Parade one. I simply flipped this to the (existing) paragraph about the (much better known) Parade one, with one minor change to make it less POV (in the same direction as JeffJor's subsequent edit). Here's a diff to an earlier version [1]. -- Rick Block (talk) 05:32, 21 December 2009 (UTC)

Rick said "I didn't 'reword' anything ... with one minor change to make it less POV same direction as JeffJor's subsequent edit." Ignoring the self-contradiction, your rewording was in the opposite direction. You added "Some of the controversy was because the Parade version of the problem leaves certain aspects of the host's behavior unstated." You said this as though it was a significant portion of the controversy, which is what MvS specifically denied and what you have no support for. The only thing that contributes to the controversty soem have called "The Parade affair," which is the controversy meant here, is the unintuitive result. You left out the parts that said the problem statement was perfectly clear for the forum in which it was published, which is the "direction of my edits." JeffJor (talk) 12:46, 21 December 2009 (UTC)

I have also had many discussions with Rick where I find his interpretations of events that we both witnessed as they occurred, or of Mathematical concepts, or of WP policies to be 180 degrees apart from mine. Glkanter (talk) 12:56, 21 December 2009 (UTC)

Sorry, wrong diff. The version I started with was this one. This is the correct diff [2]. I changed "A well-known, though ambiguous (Seymann 1991), statement of the problem was published in Parade magazine:" to "A well-known statement of the problem was published in Parade magazine:". The "Some of the controversy" sentence is in both what I started with and your subsequent edit. In general, references do not belong in the lead (see WP:LEADCITE). -- Rick Block (talk) 15:09, 21 December 2009 (UTC)

I don't care what the diff is, Rick. If you edit a paragraph that has two known flaws in it, and take out only one flaw, you are tacitly approving the other. There is no documented evidence that the MvP statement generated that controversy. She denied it was a signifcant factor. Others inserted the possibility (not the controversy), by failing to interpret the Whitiker statement as it was clearly intended. That means no alternate host strategies, and no probabilities that differ by door number alone. So you can solve the problem by UA/SCA, which are equivalent as G&S said. The only place where any controversy has arisen surrounding anything besides UA/SCA is HERE. That isn't NPOV. It is OR. It does not come from any of your references, because they never said what q was. They only said there ewas a potential for it to make a difference, but it didn't affect the answer. JeffJor (talk) 17:29, 21 December 2009 (UTC)

I agree intuition is the problem and that rigor is not the answer. IMO (this is WP:OR) the problem statement deliberately forces the reader to think about the specific conditional case where door 1 has been picked and the host has opened door 3, so the player is now looking at two specific closed doors and an open door. And, yes, this case is used as an example.

The salient features of this case (which apply to any other) are 1) the player doesn't know where the car is with certainty, and 2) there are only two possible choices. The "equal probability" assumption (cf. Falk or Fox and Levav) strongly leads people to the conclusion that the odds must be 50/50 in this case, and therefore any other equivalent case. Note that this reasoning starts with a specific conditional case, and then extends to the unconditional answer not the other way around.

The unconditional solutions ignore the specific conditional case the problem statement has forced the reader to think about, and jump straight to the (correct) unconditional answer. However, they NEVER reconnect back to the original conditional case—that is, these solutions do not address the mental model most people construct which led them so convincingly to their initial 50/50 conclusion. This is basically a bait and switch approach, leaving people with two choices - trust their "equal probability" intuition, or believe a solution that seems to be true but doesn't specifically address why or how their intuition failed. I think this is precisely what leads to many of the arguments over this problem. Most people are very reluctant to abandon what they see as an intuitively obvious answer. The unconditional solution approach tries to lead people to a different mental model. The other alternative is to address the conditional case head-on, and explain why even in this case the odds are 1/3:2/3. I would like the article to do both of these, in one solution section. As Boris says "The coexistence of the conditional and the unconditional can be more peaceful". -- Rick Block (talk) 21:27, 19 December 2009 (UTC)

Does anyone object to Formal Mediation?

"Mediation is a voluntary process in which a neutral person works with the parties to a dispute. The mediator helps guide the parties into reaching an agreement that can be acceptable to everyone. When requesting formal mediation, be prepared to show that you tried to resolve the dispute using the steps listed above, and that all parties to the dispute are in agreement to mediate. Mediation cannot take place if all parties are not willing to take part. Mediation is only for disputes about Article Content, not for complaints about user conduct."

Formal Mediation

Please indicate below:

I am willing to take part in Formal Mediation

Glkanter (talk) 15:03, 18 December 2009 (UTC)

Rick Block (talk) 16:03, 18 December 2009 (UTC)

Martin Hogbin (talk) 16:34, 18 December 2009 (UTC)

JeffJor (talk) 16:35, 18 December 2009 (UTC)

Gill110951 (talk) 13:22, 20 December 2009 (UTC)

Colincbn (talk) 02:26, 22 December 2009 (UTC)

Nijdam (talk) 17:13, 11 January 2010 (UTC)

I am not willing to take part in Formal Mediation

Thank you. Glkanter (talk) 15:03, 18 December 2009 (UTC)

Nijdam posted an edit to this page nearly 24 hours ago. How much longer do we wait for him to indicate his decision? Glkanter (talk) 11:56, 21 December 2009 (UTC)

Nijdam posted an edit to this page over 48 hours ago. Still no comment or signature on this Formal Mediation. Can we move on without his signature? Is anybody else ready to move this forward? Glkanter (talk) 13:11, 22 December 2009 (UTC)

I thought we were proceeding. This seems much more important than the RfC below. Martin Hogbin (talk) 13:15, 22 December 2009 (UTC)

Well, we were. But there's no Formal Mediation unless everyone agrees to it. I see us as stuck, for no apparent reason.

Yes, that RfC is a distraction. Unfortunately, for me, anyways, it has to be dealt with seriously. I knew this was coming the minute he vandalized my talk page edit, and begged Dicklyon to let me edit my own section as I had written it. All to no avail. So it goes. Glkanter (talk) 13:23, 22 December 2009 (UTC)

The parties that need to agree are the parties listed in the request for mediation. As far as I know this does not exist yet. After creating such a request you notify the named parties about it, see Wikipedia:Requests for mediation/Guide to filing a case. Pre-agreeing to mediation here is nice, but ultimately irrelevant. The parties named in the informal request were Martin, Jeff, Glkanter, Nijdam, Kmhkmh, Father Goose, and myself. I've been assuming Glkanter or Martin were working on a formal request. If this is not the case I'd be willing to write one up, although if someone else would prefer to do this that's fine with me. I might suggest Martin. -- Rick Block (talk) 17:09, 22 December 2009 (UTC)

It would have been nice of you to present this view either when you signed, or instead of signing, back on the 18th. Why go to all the effort of creating a request until Nijdam, and Kmhkmh indicate they will go along with the decision? I have serious doubts that Nijdam will agree. How hard can it be for them to say? Just more stalling of the inevitable. Excellent job this time, Rick! Glkanter (talk) 17:23, 22 December 2009 (UTC)

Based on the level of hostility you've exhibited toward me, I thought you would prefer someone else write up the mediation request. That's what this edit (from last Thursday) meant, where I provided a link to the appropriate procedure. I assumed you'd read this and that you or Martin were working on it. Per below, Martin is OK with me writing it up. Are you? -- Rick Block (talk) 20:09, 22 December 2009 (UTC)

Martin also wrote this in the very next sentence in the paragraph (below): "If you want me to do it let me know and give me some clues what to do." I like that better, thank you. I don't see myself as hostile. Just honest. And fed up. Glkanter (talk) 20:23, 22 December 2009 (UTC)

Rick, I am not familiar with the procedure, and would be quite happy for you to do it. If you want me to do it let me know and give me some clues what to do. Martin Hogbin (talk) 17:56, 22 December 2009 (UTC)

Informal mediation still a possibility

I note that User:K10wnsta has offered to serve as an informal mediator for the case at Wikipedia:Mediation_Cabal/Cases/2009-12-06/Monty_Hall_problem#Discussion.

If nobody had an objection to proceeding with the case at that venue, it would probably allow things to get under way sooner.--Father Goose (talk) 04:19, 24 December 2009 (UTC)

Re: Wikipedia:Mediation_Cabal/Cases/2009-12-06/Monty_Hall_problem

In my brief overview (I haven't delved into archives), the discussion appears to have remained civil and, more important, cooperative in seeking a means of negotiation. If everyone is willing to excuse the sluggish response to your request for informal mediation (blame it on the holidays ;) ), I'd be happy to work with you in resolving the dispute. However...
You waited over two weeks for assistance at MedCab and, procedurally, are justified in pursuing formal mediation. If someone has already applied significant effort in preparing for that, I understand if you wish to continue in that direction.
--K10wnsta (talk) 20:29, 25 December 2009 (UTC)

There are 11 archives to this discussion, covering 6 years. While technically 'civil', it is very contentious. I appreciate your offer to help, but I'm not sure there would be a result worth the time investment you would need to make. Honestly, if I may, your original comment about this puzzle being 'mathy' did not create confidence in this reader. And I'm the least Mathematics educated person on this talk page.

But, this is just one person's opinion, offered in good faith. I'd hope I can support whatever the consensus decides on your generous offer. Glkanter (talk) 17:33, 26 December 2009 (UTC)

Hehe, well, the 'mathy' description stemmed from reading about a dispute involving 'mathematical sources' and 'conditional probability' in what appeared to be an article about the host of a campy game show. I couldn't fathom how the subjects were related (and even questioned my recall of the host's name). It was certainly not intended to express any personal disdain for mathematics - in fact, I enjoy and excel in most math-related fields (notably algebra, geometry, and statistics).
--K10wnsta (talk) 21:07, 28 December 2009 (UTC)

As one of the long term involved editors I would welcome some mediation. I am not sure what your understanding of maths and probability is like but the Monty Hall problem has been described as the world's most tenacious brain teaser. It will therefore be necessary for you to first get your head round the basic problem, if you are not already familiar with it. Note that nobody here disagrees with the basic numerical answer under the 'standard rules'.

If you proceed with mediation, it would be interesting for you to start by reading the article (or possibly a previous version ) through to see how good an understanding of the problem it gives you before consulting other sources or talking to anyone about it, as the debate is essentially about how well this article addresses the basic problem. You currently have the advantage of seeing this article as a newcomer but once you have been drawn into the debate you will quickly lose that viewpoint. This suggestion is not intended to be an attempt to 'get in early' with my POV. Perhaps someone on the 'other side' could confirm that they would be happy for you to take this approach. Martin Hogbin (talk) 11:02, 28 December 2009 (UTC)

I have read the article and now understand how Monty Hall could be associated with conditional probability (see my reply above). I haven't yet delved into the actual dispute as I prefer remaining sequestered from it until we get past the informal formalities (eg. all interested parties agreeing to participate in the mediation process).
--K10wnsta (talk) 21:07, 28 December 2009 (UTC)

Kanov Is Wrong

The article states (without citation) that Kanov stated that in the "Ignorant Monty" case, swapping still yields a 2/3 chance of winning - but a quick simulation of all cases reveals this to be wrong: suppose I pick door 1, and Monty opens door 2 without knowing what is there but reveals a goat (all other permutations are equivalent to this): the car will now be behind either door 1 or door 3 with a 1/2 probability. --New Thought (talk) 09:44, 19 December 2009 (UTC)

You are quite right. Because of all the argument here nobody has noticed a simple error. There seems to be a section based on a the supposed opinion of a mysterious Kanov. I will remove this unless someone can explain why I should not. Martin Hogbin (talk) 10:54, 19 December 2009 (UTC)

I've wondered about this, going back to the summer. If I recall correctly, Marilyn vos Savant says it's 1/2 because of the plays that get eliminated by Monty revealing a car. I might suggest that once the contestant is faced with the two doors and a revealed goat, it's the same 1/3, 2/3 as the original MHP. Then I have to figure out how this is consistent with Deal or no Deal, which says there is no advantage to switching.

Vos Savant is correct. If Monty chooses any unchosen door randomly you have to decide what to do if he reveals a car, asking the player whether she wants to change after a car has been revealed is pointless. Easiest would be to replay those games from the start. Games where Monty reveals a car are therefore discounted. These games can only be ones where the player has originally chosen a goat because, if the player has originally chosen the car, the host cannot reveal it. Thus in the 'Ignorant Monty' case we remove some games where the player originally chose a goat but none where she originally chose the car, thus her chance of having originally chosen the car goes up. Martin Hogbin (talk) 18:56, 19 December 2009 (UTC)

Martin - I don't think you're addressing the issue. I believe the confusing scenario is a specific show, say last Tuesday's, where Glkanter was the contestant. On this show, he's initially picked a door, say Door 1, and Monty has forgotten where the car is. He says "Oh dear, I've forgotten where the car is. I hope this works out OK - Carol, please open a random unchosen door". And, fortuitously, the door that is opened, say Door 3, reveals a goat. There is no decision about what to do if the car is revealed, because the car simply wasn't revealed. Glkanter's initial choice has a 1/3 chance of having been correct. The chance the car is behind the open door is clearly 0. The other one must have a 2/3 chance.

That is the issue I addressed. I explained why the probability that the player has chosen the car increases when Monty reveals a goat by chance. Even for the one-off case the fact that Monty has chosen randomly but in fact revealed a goat means that the player is more likely to have chosen the car. Martin Hogbin (talk) 20:15, 19 December 2009 (UTC)

Glkanter - is this more or less what you're thinking? -- Rick Block (talk) 19:41, 19 December 2009 (UTC)

Did you really do a simulation? Glkanter (talk) 14:15, 19 December 2009 (UTC)

The original sources are correct. "Kanov" is presumably the name of the anonymous editor who put this in the article (yesterday). I've reverted this change.

Glkanter - the probability this is talking about is precisely the one applying to the contestant faced with two doors and a revealed goat (in a case where the host has randomly, but successfully, opened a door revealing a goat). Perhaps Martin or JeffJor could explain to you why the "combining doors" solution (or any of the other unconditional solutions) do not apply, and why the probability is indeed 1/2 in this case. This is not a sarcastic suggestion - I could try to explain it but I doubt that you'd be willing to listen to me. -- Rick Block (talk) 17:24, 19 December 2009 (UTC)

It's a different problem, what you call a 'variant'. I offered my two cents on a talk page. I figured I might regret it. Glkanter (talk) 17:42, 19 December 2009 (UTC)

Even though this problem is always described as "counter-intuitive", I find it interesting that EVERYONE on Earth understands the problem intuitively if you look at it another way: When you watch Deal or No Deal, the only reason it's suspenseful is because the person opening a case does NOT know if there's a big number inside that case. If you were on a Monty Hall Problem game show, and picked door #1, and the host said "I'm going to open a door now... hmmm... number 2" (ignorant monty - or at least from the player's POV, you must assume ignorant monty), you would be worried and suspense-filled that he might open the door with the car. When he doesn't, you feel relief. However, if Monty said, "Now, let me open a door with a goat in it... number 2" you would feel no suspense. He has told you the door has a goat, you know it's a goat, and it has no suspense. This is because there is no risk in him opening a door. He will always open a goat door. If your odds of having a goat behind your original selection improved, you'd be excited after he revealed a goat, but because he knows it's a goat, you feel no more excited about your first choice than before he opened the good. This is an example of how people DO intuitively understand this, but then don't recognize the ramifications of this feeling when offered the choice to switch observe below:

Interesting. Martin Hogbin (talk) 20:19, 19 December 2009 (UTC)

Here is an analysis of all cases when the car is behind Door number 3 (logic dictates that there are tables for the car behind behind doors 1 and 2 that have identical probabilities (for the appropriate doors). The number at left is the door you choose; the number at the top is the door Ignorant Monty opens. The result is whether you should switch ("y" or "n"). "c" represents Monty revealing the car.

	1	2	3
1		y	c
2	y		c
3	n	n

1,1 2,2 and 3,3 are greyed out, because he can't open the door you chose. As you can see, there are two cases where switching nets you a car, and two cases when it does not. There are also two cases where he reveals the car ("c") and you are (presumably) not offered a choice, as the car location is now known. Ignorant Monty has a 1/3 chance of revealing a car and ending the game. ONCE that does not happen, there are four possible cases left, 1/2 of which require switching to win, 1/2 of which require keeping to win. This is the conditional probability of "What is the probablity that switching will win GIVEN that Montry did not reveal the car?" The absolute probability is absolutely true - even with ignorant Monty, switching will win you the car 1/3 of the time - 1/3 of the time staying will win, and 1/3 of the time Monty will reveal the car, and you will not get the option.

Regular Monty has 0 chance of revealing a car. While regular monty has a decision to make SOMETIMES (if you select the car, he must pick which goat to reveal), as long as his pick is random, the result of his pick are both the same: you should still not switch, (so the conditional probability of winning by switch IF monty randomly selects one door or the other is 0 in both cases - you can't win by switching). Thus, if you picked right the first time, don't switch. If you picked wrong the first time, DO switch. Therefore, 1/3 of the time, don't switch, 2/3 of the time, switch.

This is true in the ignorany monty case also: If you picked wrong (2/3), do switch. If you picked right (1/3) don't switch. However, half of the time when you pick wrong (half of 2/3 = 1/3), Monty reveals the car, and you don't get to make a choice. Therefore, IF you get the option to switch (only 2/3 of the time will you get this far), then the odds are even between keeping (1/3) and switching (1/3) (the other third is monty reveals the car). TheHYPO (talk) 19:47, 19 December 2009 (UTC)

As a PS: I thought I'd explain the difference in why one is conditional and one is not: remember that if you have four cases: in order to say that any of them has a 1 in 4 chance of occuring, there MUST be an equal chance of each occuring. In the original monty hall problem (let's say car is behind door 3):

1. If you pick door 1 (1/3 chance), he MUST open door 2 100% of the time (thus, also 1/3 chance).
2. If you pick door 2 (1/3 chance), he MUST open door 1 100% of the time (thus, also 1/3 chance).
3. If you pick door 3 (1/3 chance), he could open doors 1 or 2 (if he picks randomly, 50% chance of either).

As you can see, your choice of doors all have an equal 1/3 chance of occuring, there are four 2nd step cases ([you:1 monty:2], [you:2, monty:1], [you:3, monty:1], [you:3, monty:2] with DIFFERENT probabilities of occuring (1/3 each for the first two - both of which say "switch", 1/6 each for the second two - both of which say "don't switch"). Thus some people claim that logically, two of those four 2nd step cases say "switch" and two say "stay" - that's 50/50. But two cases occur half has often has the other two. In the Ignorant Monty problem, all 6 cases in my table above are equal probability (1/6). This is because when you pick a "wrong" door, he has two options, not one. so your 1/3 choice results in two 1/6 choices for Ignorant Monty (one of which reveals the car and ends the game). If he DOESN'T reveal a car, you're left with four cases with initial probability of 1/6, and thus, each case NOW has a 1/4 chance (two win by switch, two lose by switching, thus 1/2 chance of winning by switching.) TheHYPO (talk) 20:08, 19 December 2009 (UTC)

Technology required new section.

I believe I correctly summarized vos Savant.

Let's re-apply some things we've learned: 'Suppose you're on a game show...' Still true? Contestant's SoK? 'Random' would equal Deal or No Deal. 'He's drunk' or 'forgetful' might not be communicated to the contestant. Then it's still the MHP from the contestant's SoK.

What exactly is the revised problem statement? —Preceding unsigned comment added by Glkanter (talk • contribs) 20:04, 19 December 2009 (UTC)

The probability from the contestant's point of view depends on the contestant's knowledge of the game rules. If the contestant is told the host knows what is behind the doors and will always choose a goat then the probability of winning by switching is 2/3 from the contestant's POV (SoK). If the contestant knows the host is choosing another door randomly (and then is relieved to see a goat revealed - see comment above) the probability of winning by switching is now 1/2. Is that your understanding? Martin Hogbin (talk) 20:28, 19 December 2009 (UTC)

By 'random' I mean 'car or goat revealed by Monty'.

I don't thìnk your summary or Rick's summary reflect my thoughts on this puzzle. Have I been obtuse? Why summarize me at all? —Preceding unsigned comment added by Glkanter (talk • contribs) 21:03, 19 December 2009 (UTC)

It was meant to be an explanation of why the probability of winning by switching is 1/2 if the host chooses an unchosen door randomly (that is to say he might choose a car or a goat). You seemed uncertain as to whether you agree with this statement. Do you agree? Martin Hogbin (talk) 21:16, 19 December 2009 (UTC)

If the contestant is informed (that is, it's a premise of the puzzle) that the host is opening doors randomly, and may reveal a car, then it's Deal or No Deal. Rick had a very elaborate scenario for the 'drunk' or 'forgetful' Monty. What is communicated to the contestant prior to his decision? Is this still a game show, then? How is it stated as premises?

I'm just pointing out that 'random', or 'forgetful' still require 'formalized' problem statements, which may be different. Absent that, either, or any answer may be correct. I'm not real good at multi-tasking. I just had some thoughts that could have developed into something. But until we have the underlying MHP squared away, I find this personally distracting. Glkanter (talk) 21:27, 19 December 2009 (UTC)

Many more words

Until now only Boris has shown the derivation of a solution in formulas, using symmetry. This leads to the conclusion - as I BTW showed a million comments ago - that the conditional probability we are interested in is equal to the unconditional and hence may be easily calculated. It doesn't show the conditional probability is not needed. All others come with words, words, .... Nijdam (talk) 17:25, 20 December 2009 (UTC)

Yes, Nijdam, too many words. How about your signature agreeing to Formal Mediation? Glkanter (talk) 17:33, 20 December 2009 (UTC)

There are so many words here because people don't explicitly state the assumptions they use to get their solution. Conditional and unconditional probabilies are equal and easy to find by symmetry in a special, nice, symmetric case. I took a look at the Selvin paper. I like the intro very much indeed, I don't like the solution. He does not say in advance what assumptions he is making, you can only guess them by studying his proof. He enumerates the cases and solves the problem by counting. This means that he is assuming that all cases are equally likely. This means that he is assuming the car-key is hidden uniformly at random, that the quiz-player chooses a box uniformly at random independently of the location of the key, and that the quiz-master opens a box uniformly at random out of those available to him, given the previous two choices. Why I don't like Selvin's solution? Because it depends on his strong assumptions. We only need to assume that the first box you pick has 1/3 probability of having the key, in order to guarantee that always switching gives you 2/3 probability of ending with the key. Proof: everytime you would have got the key without switching you don't get it with switching, and vice-versa. I guess that most players think that they have a 1/3 chance of picking the right box first time. Whether or not this is true could be empirically verified. This is both real and theoretical game theory. Gill110951 (talk) 06:06, 22 December 2009 (UTC)

Words, words, ... Gill, why don't you show me your assumptions and proof in proper terminology? May be the terminology I proposed somewhere above. Nijdam (talk) 19:21, 23 December 2009 (UTC)

How About A Temporary Editing Freeze On The Article

I don't understand why all this article editing is taking place without being discussed.

While we 'old guys' are working towards a formal WP solution, newer people are editing at will.

This seems unproductive, not good for the article or readers, and distracting.

Any support for a temporary freeze? Is this even plausible? Thanks. Glkanter (talk) 12:25, 21 December 2009 (UTC)

I think it would be wise for editors to wait, as after mediation there may well be major changes (I hope) and they would the be wasting all their effort. Martin Hogbin (talk) 15:31, 21 December 2009 (UTC)

I guess I am "a newer person, editing at will". My excuse: when I see factual incorrectness or incompleteness in the existing article I make small edits - I don't touch the main structure. I obviously won't/can't object if those contributions get thrown out later. What I do like is the draft construction page, http://en.wikipedia.org/wiki/Talk:Monty_Hall_problem%5CConstruction That seems to me to be a very useful step: make a fresh start aiming to accomodate the various opinions which are around. It is precisely because there are so many different ways to formulate a Monty Hall problem that it is so attractive. Gill110951 (talk) 19:35, 21 December 2009 (UTC)

Why not use the current version as the starting point for the construction page? Then all edits will be in a clear audit trail for all to see. Glkanter (talk) 20:02, 21 December 2009 (UTC)

Rick Just Filed This RfC On Me

RfC Glkanter

He's expecting Dicklyon to 2nd it. I see a lot of unintended irony here. I had just created a new section on the talk page with 3 edits. Then, here's what I call Dicklyons's unprovoked vandalism on my talk page edits:

(Reverted 1 edit by Glkanter; Obviously incorrect, pointy addition, bordering on vandalism.

declutter a bit

*Roughly*

It's all right here: Is This Chronology Correct?

So, if anybody wants to put in a good word for me, I'd be much obliged. Please note, I'm pretty sure I will get this promptly dismissed, but any support is appreciated. Glkanter (talk) 04:25, 22 December 2009 (UTC)

Anyone unfamiliar with this process might want to review Wikipedia:Requests for comment/User conduct/Guidance2. It is certified now which means it won't be closed until the criteria at Wikipedia:Requests for comment/User conduct/Closingis met. Anyone is welcome to comment. -- Rick Block (talk) 05:41, 22 December 2009 (UTC)

On this RfC/U, Rick Block and Dicklyon are trying to make a case that I am disruptive, don't edit the article often enough(?),incivil, interrupt consensus building, chase other editors away, contribute nothing of value, too aggressive with my POV, have bad breath, etc. I'm holding my own on the RfC. It's gotten pretty ugly. So, if anybody would like to drop a supportive word about good ol' Glkanter, now would be a good time. By reading the RfC, you will also learn a lot about the inner thought processes of some well known editors. Thanks. Glkanter (talk) 22:22, 26 December 2009 (UTC)

Please see this new section on the Arguments Page

Huckleberry Opportunity

Thank you. Glkanter (talk) 15:10, 23 December 2009 (UTC)

I'll Bet That 'Paradox' and 'Game Theory' Are Mutually Exclusive And Opposites

I think there are 2 POVs regarding how to 'cherish' the MHP paradox.

Some of us, including myself, love the simplicity. Nothing happens. Heated Arguments over 1/2 vs 2/3 ensue. More than once, even.

Other people like the complexity, and 'what ifs' that the MHP could be with just a little tweaking. The permutations can approach Game Theory scenarios.

Since it was a great paradox before Morgan and conditional, I consider the 'simplicity' people the ones who accurately support how Selvin's MHP paradox should be presented in the Wikipedia Article. Glkanter (talk) 15:35, 23 December 2009 (UTC)

There's Only 2 Things Being Debated Anymore

1. The simple solutions are not solving the correct problem.

2. Morgan's paper, published in 1991, can claim to recognize and describe the Monty Hall Problem Paradox, first published by Selvin in 1975, equally as well (and equally importantly) as Selvin's original paper, which relied only on simple solutions.

I'd like to see the people arguing in support of those 2 arguments come out and directly say it. Once you clearly state your positions, the other editors, using reliably published sources can then address your objections to the proposed changes. Glkanter (talk) 18:32, 23 December 2009 (UTC)

This Is Why They Can't Be Represented in the Article 'Equally'.

Simple solution is not a solution at all

"This is the same topic discussed in more detail three sections down (about the subtly different question), and indeed Morgan et al. argue the "simple" solution is not a solution at all." -- Rick Block (talk) 16:28, 26 October 2008 (UTC) —Preceding unsigned comment added by Glkanter (talk • contribs)

Many sources do give simple solutions but you try to use one source to veto all others by saying, 'Morgan et al. argue the "simple" solution is not a solution at all'. This is your POV but it is not what sources (note the plural) all say. Some sources give the simple solution as the correct one. These sources should be properly represented in the article. Martin Hogbin (talk) 13:42, 24 December 2009 (UTC)

I have no idea why Glkanter reposted this old quote. I think we all agree the POV of the article should not be that the unconditional solutions are incorrect. On the other hand, the article does need include the POV expressed by Morgan et al., and Gillman, and Grinstead and Snell (this is their POV - and whether any editor here agrees with it or not is completely irrelevant) that the unconditional solutions are addressing a slightly different problem than what they think the problem is. I think the only question here should be how best to do this in an NPOV manner. What I hear you (and Glkanter and Jeff) arguing is that they're wrong (sorry, per WP:OR and WP:V Wikipedia doesn't care what you think about their POV), or that their POV should be excluded (sorry, per WP:NPOV Wikipedia must include all significant views). I'd be delighted to work toward a more NPOV treatment. -- Rick Block (talk) 17:27, 24 December 2009 (UTC)

Is it typical for a FA article to need a '...more NPOV treatment.'?

You've always denied the Morgan-centric POV exists until now. How did this POV get into the article? How do we make sure this doesn't happen again? Shouldn't somebody be in big trouble for editing in these violations of WP:NPOV? Glkanter (talk) 18:03, 24 December 2009 (UTC)

This is yet another example of exactly the kind of disruptive behavior Wikipedia:Requests for comment/Glkanter is about. I'm offering to help you achieve your goal. What would you say you're doing? I'd call it trolling. I can't speak for anyone else, but I'm extremely tired of it. Please stop. -- Rick Block (talk) 19:53, 24 December 2009 (UTC)

Actually, Rick, this is another example of you claiming whatever fits your current needs. Here you sound the alarm about the potential for the article to have a POV Last Paragraph. As if the Wikipedia world as we know it would collapse if that happened. But, when you acknowledge that the article currently has a Morgan POV (above), you're not quite as concerned about fixing it in a timely manner. Glkanter (talk) 22:47, 24 December 2009 (UTC)

@Rick, you seem to be putting up an Aunt Sally (Strawman argument). You seem to be implying that I want to remove the POV of Morgan and others who agree with them from the article. That is not the case. I have always suggested that the article should start with the simple non-conditional solutions and then, after discussing these thoroughly, move on to the conditional case discussed by Morgan and others. It is clear, from your reposted quote above (I had not noticed that it had been reposted) that you believe that the Morgan paper should somehow veto or overrule all other sources no matter what they say. Martin Hogbin (talk) 22:54, 26 December 2009 (UTC)

Am I somehow not being clear here? What I believe is that the article should represent as a POV what it is that Morgan et al. (and Gillman, and Grinstead and Snell) say. What they all say is that the unconditional solutions don't exactly address the problem. Morgan et al. go so far as to say the "simple" solution is a "false" solution. In the quote above, I'm saying that Morgan et al. say this, not that I think this POV should veto or overrule all other sources. Whether you agree with what they say or not, do you at least agree that this is what these sources say? I assume you understand that saying that these sources say the simple solution is no solution is not the same as the article taking this as its POV. -- Rick Block (talk) 00:21, 27 December 2009 (UTC)

I am fine with Morgan's POV in the appropriate place but not in the simple solution section. Martin Hogbin (talk) 17:51, 3 January 2010 (UTC)

There's a huge dichotomy between what you write above, Rick, and how you've edited and protected Morgan's POV throughout the article, even down to the FAQs. Plus, it contradicts your long standing and still existing arguments that Morgan's, as the sole peer-reviewed source, is the prevailing POV, and deserves prominence in the article. Plenty of sources apparently don't find Morgan's arguments all that convincing, as they keep publishing simple solutions. I'm not publishing them, professionals are publishing them. It's not my POV, it's the sources' POV. That's why there is an 'editing' function required more so for some articles than others. Editing means more than proper footnoting. And sometimes it means telling a story as it happened, chronologically. That's not POV, that's editing. Glkanter (talk) 18:18, 3 January 2010 (UTC)

I Guess I'd Better Start Editing The Article

In the RfC that Rick Block and Dicklyon filed on me RfC Glkanter one of the 'complaints' was that I argue on the MHP talk pages too much, at the expense of actually editing the MHP article. The associated 'remedy' was that I modify the MHP article more frequently and discuss my reasons for doing so less often.

Now, that's no reason to slap me with an RfC, but the point is well taken. I've asked for a 'freeze' on the article of some sort at least twice in the last couple of weeks. Meanwhile, some editors just make edits without discussing them first.

So, consistent with my stated understanding of the various literature on the MHP, and in accordance with Rick's criticism/suggestion as conveyed via Wikipedia's formal RfC procedure, I will begin to thoughtfully edit the article as I understand the consensus has approved. Glkanter (talk) 15:51, 24 December 2009 (UTC)

How about I start with the FAQs on the talk page? That looks like pure Morgan POV, a clear violation of NPOV. Anybody want to clean it up, or should I just delete it? Glkanter (talk) 16:47, 24 December 2009 (UTC)

I'm sorry, but how do you find the FAQ a "clear violation of NPOV"? Would it help if it said "according to these sources" a couple of times? There is no particular requirement that talk page FAQs adhere to NPOV, but I'd be happy to work with you to make this more NPOV if it bothers you (which it clearly seems to). -- Rick Block (talk) 17:39, 24 December 2009 (UTC)

No thanks. I'm going to use the RfC as an opportunity to learn. Since you feel I should be sanctioned because I've only made '6 article edits out of about 1000 talk page edits', I'll go it alone, without all that 'discussing' you find so offensive from me. Glkanter (talk) 22:39, 24 December 2009 (UTC)

The first two lines address FAQs. The rest is yet another lengthy defense of Morgan. NPOV is not a requirement for FAQs? That seems to contradict Wikipedia's bedrock policy. Can you provide a link that supports your POV? Glkanter (talk) 14:13, 25 December 2009 (UTC)

Here's another one. Id like to change the 'Simple solution' heading to something like 'Original Paradox explanation' or 'Selvin's Proof' or 'vos Savant's Popular Solution'? I'd like to get the point across concisely that it was this level of understand from which all the excitement about the paradox came. Not to be confused with the 'conditional solution' or, non-solution without the equal goat door constraint being equal to exactly 1/2, that came out some 15 years later. Glkanter (talk) 16:03, 25 December 2009 (UTC)

Then a transition section that says 'For many people, this is all the understanding they need, and was Selvins and vos Savant's point. Others may want to continue further into this article...' And as long as there's no bad-mouthing the 'original' solutions, you 'conditional' guys can pretty much do what you want with the article from there. Glkanter (talk) 16:10, 25 December 2009 (UTC)

FAQ page boilerplate

This is most of the 'greeting' to the talk page of the FAQs. Probably only seen by other editors.

"This page is an FAQ about the corresponding page Monty Hall problem."

"It provides responses to certain topics being brought up again and again on the talk page, sapping many editors' time and energy by forcing them to respond repeatedly to the same issues. The FAQ addresses these common concerns, criticisms, and arguments, and answers various misconceptions behind them."

I think this can be improved. Anybody mind if I take a shot at it? Glkanter (talk) 23:32, 26 December 2009 (UTC)

This is standard boilerplate from Template:FAQ page. Are you suggesting changing the standard boilerplate (used on over 100 pages) or replacing the standard message with something custom for this page? -- Rick Block (talk) 00:29, 27 December 2009 (UTC)

I guess this is why we discuss things. I don't like the phrasing. Maybe the words in the box were only meant as an example? Glkanter (talk) 01:12, 27 December 2009 (UTC)

It's a variant of template:FAQ, one of many templates intended for use on talk pages. See Wikipedia:Template messages/Talk namespace. Template:FAQ2 is another version. - Rick Block (talk) 01:58, 27 December 2009 (UTC)

The 2 FAQ templates don't strike me as civil. Is there a rule against changing the text inside the box? Maybe it was just sample text? Glkanter (talk) 02:36, 27 December 2009 (UTC)

No, there is no rule against changing the text in templates. I'm sure there are plenty of people who have these templates on their watchlists. If you make a change anyone objects to they'll revert it. Whatever change you make will show up on every talk page the template is used on, so don't change the text to be less generic. -- Rick Block (talk) 05:01, 27 December 2009 (UTC)

You're saying that by changing the text in the MHP FAQ text box template, this will back-propogate to all users of that template? I wouldn't have expected that. Is that theory, or experience that informs you? Glkanter (talk) 06:26, 27 December 2009 (UTC)

I'm saying if you edit template:FAQ page the text will appear on any page that transcludes this template (anything marked as "transclusion" here). This is a feature of the MediaWiki software used to run this site. This is both theory (in the sense that it is a known feature of the software) and something I have personally experienced, many hundreds of times. -- Rick Block (talk) 18:50, 27 December 2009 (UTC)

I appreciate your help with this, Rick. I'm suggesting we would edit this. What then? Glkanter (talk) 19:27, 27 December 2009 (UTC)

If you edit Talk:Monty Hall problem/FAQ and change

<noinclude>{{FAQ page}}</noinclude>

to something else, e.g.

<noinclude>blah blah blah</noinclude>

"blah blah blah" will only show up on the MHP FAQ page. However, because the text you're talking about is inside the "noinclude" tags it does not appear when you're viewing this page (Talk:Monty Hall problem), even if you click the "show" link at the top of this page (scroll up to the top of this page and try it!). The bottom line is you only see this text if you're editing the FAQ page (and previewing your edit), or directly viewing the FAQ page as opposed to the talk page (there's no link to it, so I'm not sure how this would happen). I might suggest that whatever you think of this text, it's not worth worrying about. -- Rick Block (talk) 19:56, 27 December 2009 (UTC)

Variants

Variants - Slightly Modified Problems section.

Since the MHP is from the contestant's POV, there should be some narrative about what the POV's in this whole section represent. Are they the contestant's? Is it a premise in each different problem that it's no longer the contestant's POV? What about addressing the Monty Hall problem from 'not-the-contestant's POV' for comparison purposes? This would be beneficial to the readers, I believe. Glkanter (talk) 16:55, 27 December 2009 (UTC)

Can we call this "state of knowledge", not "POV" (to distinguish from the local Wikipedia meaning of POV)? In all cases what is meant is the probability given everything included in the problem statement. This is perhaps most literally the SoK of the puzzle solver, but presumably matches the contestant's SoK as well. The "MHP" is also from the puzzle solver's SoK, so there's really no difference. If this is not clear it wouldn't hurt to try to clarify it, but I don't think anyone should be confused about this since it is how mathematical word problems are universally treated. If it's important to the problem to take some particular perspective, the problem says to. For example, in vos Savant's "little green woman" scenario [3] if the player has picked door 1 and the host has opened door 3 we (the puzzle solver) know the probabilities are split 1/3 (door 1) and 2/3 (door 2) but the question is what are the little green woman's chances of randomly picking the door with the car, not what is the probability the car is behind door 1 or door 2. -- Rick Block (talk) 19:28, 27 December 2009 (UTC)

In Selvin's and vos Savant's MHP, what the reader knows and what the contestant knows are both consistent with "Suppose you're on a game show..." Every host/producer decision is described as 'random'. That's no longer true with the 'variants' where the reader becomes aware of some host bias. The contestant, of course, cannot. Hence, I disagree with your above explanation.Glkanter (talk) 19:37, 27 December 2009 (UTC)

Editing the MHP FAQs

Rick, the current text includes this:

"The point of introducing this variant is to show the difference between the unconditional and conditional questions. In this variant, these questions have different answers exposing the difference between unconditional and conditional solutions."

I still disagree that using a different problem is a means of challenging a particular problem. Originalists would argue that all you've demonstrated is the difference between puzzles with different premises. I would further argue that with the contestant being aware of Monty's left door bias, this is no longer the MHP about a game show that Selvin and vos Sovant made so famous. Glkanter (talk) 06:38, 27 December 2009 (UTC)

Are there 3 published solutions?

Selvin's - simple: 2/3 & 1/3, always switching doubles your likelihood of getting the car
Morgan's - conditional, no symmetry: between 1/2 and 1 (?), never to your disadvantage to switch
Morgan's - conditional, with symmetry: 2/3 & 1/3, always switching doubles your likelihood of getting the car

Have I summarized the above properly? Glkanter (talk) 11:03, 27 December 2009 (UTC)

If so, maybe the article could transition from:

Simple, to conditional - with symmetry (they are equivalent), to conditional - no symmetry (leftmost door variant). Glkanter (talk) 11:30, 27 December 2009 (UTC)

This is the current structure of the article, so I don't get what you're suggesting (change the article to be like the article?). The conditional with symmetry solution dates to Selvin as well. -- Rick Block (talk) 20:24, 27 December 2009 (UTC)

Rick, rather than make controversial changes or deletions to the article's text, I am trying to make it clearer to the reader how the whole 'Morgan' controversy started. I thought Morgan's whole point was that Selvin and vos Savant overlooked something? So, I'm just suggesting to actually add a 3rd solution section, for increased overall clarity. Glkanter (talk) 20:41, 27 December 2009 (UTC)

Some questions for you all

In an attempt to see exactly who thinks what I have set up some questions on User:Martin_Hogbin/Monty_Hall_problem/dissenters. Everyone is welcome to add their answers. Please comment briefly only in the comment section and have discussions about the questions on the associated talk page.

Whether we have external mediation or not I am sure it will help if everyone answers the questions on this page. I am trying to determine of we have two distinct camps, a single axis of opinion, or just randomly scattered views on the subject. Are there any other questions that editors feel will help sort out the differences of opinion here? I have just added a few extra ones. Martin Hogbin (talk) 11:36, 28 December 2009 (UTC)

Is the term 'Variant' as used in the MHP a common usage?

I disagree with your recent reverts to the article, Rick.

I just checked the Morgan paper, and they do not use the word 'variant' or any derivative of it when describing the problems.

I think this is an uncommon usage, and does not clearly indicate to the reader exactly what is being described. I don't think adding 'Slightly Modified Problem' to a heading, and replacing 1 instance of 'variant' in the article also with 'slightly modified problem' is 'pointy'. Different than your POV, perhaps, but that does not necessarily make it, or any other edits I may make in good faith, 'pointy'. Glkanter (talk) 19:45, 27 December 2009 (UTC)

Yes, "variant" is common usage. Pointy was referring to the dates. Sevlin's 2nd letter has a conditional solution, so saying the "probabilistic" solution dates from 1991, or is not the "original" solution, or addresses only a variant is a clear attempt to diminish this solution which is not only a violation of NPOV but is factually false. I would appreciate it if someone (anyone) would revert this change. If Glkanter reverts again without further discussion here I'll report him to Wikipedia:Administrators' noticeboard/Edit warring for edit warring. -- Rick Block (talk) 20:15, 27 December 2009 (UTC)

What's Wrong With Adding Dates For Clarity?

Explain the problem to me please. Glkanter (talk) 01:45, 28 December 2009 (UTC)

Per above, the date you're adding for the conditional solution is simply wrong. Both the "popular" (unconditional) and conditional solutions date to 1975, both to Selvin. If you're going to add dates, you need to add 1975 for both which makes it completely redundant. You seem to be trying to insert your completely made up chronology (#Is This Chronology Correct?) into the article. -- Rick Block (talk) 04:31, 28 December 2009 (UTC)

So this whole time 'conditional v unconditional' has really been 'Selvin v Selvin'? No way. That's never been your stated intent. Or the way your POV article is written. It's always been 'Morgan v Selvin/vos Savant'. Adding two simple dates to two headings makes it clear where it all started. And it wasn't with Morgan. So the dates help the reader, and do not hurt the article. Your response is not credible based on your previous arguments for many years. Glkanter (talk) 12:56, 28 December 2009 (UTC)

Rick, you have already acknowledged a Pro-Morgan POV in the article. And offered to help me edit. Why must you continue to confound my very modest efforts at improving the article by removing this POV? Clarifying what a so-called 'variant' is and adding dates are non-antagonistic efforts to improve the article. They just happen to be different than your preference. Your actions, especially calling out to 'anyone' for 'revert' help seem to show ownership issues. Just let me edit out the POV in good faith, OK? Glkanter (talk) 13:20, 28 December 2009 (UTC)

This whole time, conditional v unconditional has always been different. In Selvin's second letter (which I've previously pointed you to, to refresh your memory there's a copy here), he says he received "a number of letters" including several who "claim my answer is incorrect". Like vos Savant, he says "The basis to my solution is that Monty Hall knows which box contains the keys" but unlike vos Savant he goes on to say "and when he can open either of two boxes without exposing the keys, he chooses between them at random" (emphasis added). Also unlike vos Savant he goes on to present a solution using conditional probability which he calls an "alternative solution" to the solution in his first letter "enumerating the mutually exclusive and equally likely outcomes".

The issue Morgan et al. address is that vos Savant's solution, and her subsequent defense of it, and the popular discussion at the time (1990 and 1991), completely overlooked the critical assumption that makes the unconditional and conditional solutions the same, i.e. that the host must choose between two boxes (two goats doors) randomly. Selvin knew this and acknowledged it in his second letter. Martin Gardner knew this and addressed it in his version of the Three Prisoners problem. vos Savant blew it, and both Morgan et al. and Gillman called her on it. That's what the "Morgan controversy" is about. Morgan et al. and Gillman both examine the consequences of omitting this assumption, in the process showing why it's critical and how the unconditional and conditional solutions are different. The unconditional solution is NOT saying that every player who switches has a 2/3 chance of winning, but that the average across all players is 2/3. The conditional solution shows that the chances are the same (2/3) for each player only if the "equal goat" assumption is made. Even without it, players who switch will win on average 2/3 of the time (and if they switch they're never worse off), but to say a player who picks door 1 and sees the host open door 3 has a 2/3 chance of winning by switching is a conditional statement and requires this assumption. The assumption can be explicitly part of the problem description (as per the Krauss and Wang version) or implicitly assumed because of symmetry or the principle of indifference, but the statement is still a conditional statement. I don't think ANYONE here (other than you) has ever argued against any of this.

What I said was "I'd be delighted to work toward a more NPOV treatment". This is not saying that I think the article has a pro-Morgan POV, but that I'm acknowledging that you think it does and I'd be happy to work with you to make it address whatever concerns you have. Adding dates (even if they weren't wrong) is not improving the article or addressing any POV concern. What you seem to be doing is trying to introduce an anti-Morgan POV. That's not how it works. Please read WP:NPOV again, specifically WP:STRUCTURE. You have said repeatedly [4] you want an unconditional solution first and foremost, followed by a disclaimer like "The Monty Hall problem is unconditional. That is the whole paradox; the rest is the explanation; go and learn." This would be sort of the exact opposite of editing out POV. -- Rick Block (talk) 19:08, 28 December 2009 (UTC)

Let the readers decide amongst the published papers. Just don't cloud the story with unnatural euphemism's like 'variant'. The 3 separate solution sections approach accomplishes my goal, along with dates clearly highlighting the history and clarifying what the heck a 'variant' is. That's not a POV, that's shedding light on the controversy. It just weakens your POV, so you demonize it.

But anyway, you argue whatever side of the coin is convenient for you each day. What's the point in going around further?

Editing delayed is editing denied! Glkanter (talk) 19:32, 28 December 2009 (UTC)

I've asked user:K10wnsta to drop by and say what he might be able to do as an informal mediator. I'll wait to see what he says. Do not in any way take the fact that I haven't reverted your change (again) to mean I accept it or agree with it. I think it might be helpful if some other folks would comment on this specific change as well. -- Rick Block (talk) 23:39, 28 December 2009 (UTC)

Any support for Arbitration?

I think Rick Block and Nijdam are fillibustering and ownershipping against beneficial changes to this article.

I see no point in waiting for either form of mediation unless Nijdam indicates he will accept the findings.

Rick filed an RfC against me last week, the first item of which is 'only edited the article 1 time.' Now, as you've seen yesterday, every edit I make, he or Nijdam at his request, reverts.

If at least 2 people are with me, I'll proceed. Glkanter (talk) 17:31, 28 December 2009 (UTC)

Be aware that mediation does not produce "findings". Its purpose is diplomatic -- to help the parties to find points of agreement. In the best of cases, the parties can agree upon a full course of action, thereby resolving the dispute.

I am almost certain that the Arbitration Committee would not accept the case, since this is primarily a content dispute, and ArbCom rejects content disputes flat out. Just FYI.--Father Goose (talk) 06:20, 29 December 2009 (UTC)

Father Goose, this is from the Formal Mediation page:

"Mediation cannot take place if all parties are not willing to take part. Mediation is only for disputes about Article Content, not for complaints about user conduct."

Since I asked on December 18th if there were objections, and would everyone indicate their agreement to take part, Nijdam has not responded. I felt that rendered the exercise useless.

The arbitration request would allege that Rick Block and Nijdam are using various filibustering and ownershipping techniques (for example, not replying to the Formal Mediation question) against beneficial changes to the MHP article, as desired by the consensus of editors many weeks ago. I fear some of them have lost interest because of the filibustering. Glkanter (talk) 11:01, 29 December 2009 (UTC)

I think you will find that what Father Goose says is still true. They are unlikely to even consider the case. Martin Hogbin (talk) 19:12, 5 January 2010 (UTC)

Mediation

Case link
I've re-opened the case at MedCab and volunteered to assume the role of mediator in a discussion aimed at resolving an on-going dispute here. Additionally, I've issued invitations to participate in the discussion to all involved parties listed in the mediation request. While anyone is welcome to offer input, I ask that those who participate do their best to be concise and refrain from assumption/presumption regarding other's perspectives.

As mediator, my primary goal is to step in as an uninvolved party and help find some common ground from which to proceed. It is not my task to pass judgment on anyone's opinion in the discussion and there is no 'right' or 'wrong' beyond that which is dictated by Wikipedia policy.

I have read the article and understand its subject matter and all it details. As I begin delving through the talk page archives, I'll open the discussion with a call for opening statements. If you feel any archived passages are significant in summarizing the situation, it would help to include links, but please conclude your first post with a Summary of Position (your opinion as it relates to the matter). And remember...concise ;-)
-- (talk) 05:28, 29 December 2009 (UTC)

K10wnsta, what exactly are you trying to facilitate? The original ruckus which led to the request was that perhaps 3 editors were not willing to allow a large consensus to change the article. Their reasons have been debated extensively, and imho, found wanting.

Rick wrote this on his informal mediation request:

What would you like to change about this?

"I would like the endless discussions to be settled. I would like the article to remain a featured article."

What most of us want is some measure of the three change proposals to be reflected in the article in a prompt fashion, via consensus. Is this what you are working towards? In what way? Do you have agreement from all parties that they will honor whatever comes out of this? What form will the outcome of this mediation take? Glkanter (talk) 14:24, 3 January 2010 (UTC) Glkanter (talk) 17:05, 3 January 2010 (UTC)

Nijdam's position

I want the article clearly mention the remark made by some sources that the so called "simple solution" is not complete. It doesn't need initially mentioning the technical term "conditional probability". To make my point clear: the following resoning:

The player, having chosen a door, has a 1/3 chance of having the car behind the chosen door and a 2/3 chance that it's behind one of the other doors. Hence when the host opens a door to reveal a goat, the probability of a car behind the remaining door must be 2/3.

is not complete and better should read:

The player, having chosen a door, has a 1/3 chance of having the car behind the chosen door and a 2/3 chance that it's behind one of the other doors. When the host opens a door to reveal a goat, this action does not give the player any new information about what is behind the door she has chosen, so the probability of there being a car remains 1/3. Hence the probability of a car behind the remaining door must be 2/3.

Something alike holds for the so called "combined doors solution" and most of the other simple ways of understanding. That's all.Nijdam (talk) 08:36, 29 December 2009 (UTC)

I'd like to add that the (a) MHP always involves enumerated doors and a decision to switch offered to the player after a door is opened, seen by the player who has to decide. This is in my opinion and of many (most) sources the only relevant problem.Nijdam (talk) 11:48, 31 December 2009 (UTC)

Martin Hogbin's position

The MHP is essentially a simple mathematical puzzle that most people get wrong. At least the first part of the article should concentrate on giving a simple, clear, and convincing solution that does not involve conditional probability. All diagrams and explanations in this section should not show or discuss the possible difference that the door opened by the host might make, although I would be happy to include, 'this action does not give the player any new information about what is behind the door she has chosen' as in Nijdam's second statement above. The first section should give aids to understanding and discuss why many people get the solution wrong, without the use of conditional probability. The first section should be supported by sources which do not mention conditional probability

The simple solution section should be followed by an explanation of why some formulations of the problem require the use of conditional probability, with reference to the paper by Morgan et al. and other sources. It should also include the various variations of the basic problem and other, more complex, issues. Martin Hogbin (talk) 10:19, 29 December 2009 (UTC)

Glkanter's position

I want the article to clearly mention that the remarks made by some sources, that the so called "simple solution" is not complete, is not shared by all sources. It need not mention "conditional probability" beyond saying that due to the symmetry forced by being a game show, the simple solution is equivalent to the symmetric 'conditional solution'.

I think I agree with Nijdam on the text, although they are both OR. It's consistent with my 1st talk page edit, using an IP address in October, 2008:

Monty's Action Does Not Cause The Original Odds To Change.

When Monty opens a door, he doesn't tell us anything we didn't already need to know. He always shows a goat. It makes no difference to this puzzle which remaining door he shows. So it starts out as 1/3 for your door + 2/3 for the remaining doors = 100%. Then he shows a door, but we knew in advance that he was going to show a goat. The odds simply haven't changed following his action. They remain 1/3 for your door + 2/3 for the remaining doors (of which there is now just 1).

I'd like to see 3 solution sections: Selvin's simple solution of 1975, transitions to Selvin's symmetrically equivalent conditional solution of 1975 (where the discussion of the simple solution's criticisms occurs), transitioning to Morgan's conditional non-solution of 1991.

I'd like to see the word 'variant' either stricken, or augmented by 'slightly different problem'.

I'd like to see a lot of 'blather' removed from the article. Too much time and effort is spent in the various remaining sections explaining the conditional solution, for no real reader benefit. Glkanter (talk) 10:39, 29 December 2009 (UTC)

And the 'Variants - Slightly Modified Problems' section needs work. The MHP is from the contestant's state of knowledge (SoK). The versions in this section are not. This needs to be normalized for the reader in a few possible ways: An explicit statement that the contestant is aware of these new conditions (in which case these are no longer game show problems), or the explicit statement these problems are not from the contestant's SoK, and a comparison of the MHP from a non-contestant's SoK. Glkanter (talk) 13:14, 29 December 2009 (UTC)

Rick Block's position

First, I think the basic issue is an NPOV issue. The primary question is whether the article currently expresses a "pro-Morgan" POV, i.e. takes the POV of the Morgan et al. source that "unconditional" solutions are unresponsive to the question and are therefore "false" solutions - and, if so, what should the remedy be.

There are a variety of sub-issues we need to discuss but I think the main event is how the solution section is presented. I strongly object to splitting the solution section into separate sections (this was done some time ago, well after the last FARC), which inherently favors whatever solution is presented in the first such section. I mildly object to including the "combining doors" explanation in the solution section rather than in a subsequent "aid to understanding" section.

What I would like is for the article to represent in an NPOV fashion both a well-sourced "unconditional" simple solution (e.g. vos Savant's or Selvin's) and a well-sourced conditional solution of the symmetric case (e.g. Chun's, or Morgan et al.'s, or Gillman's, or Grinstead and Snell's) in a single "Solution" section, more or less like the suggestion above (see #Proposed unified solution section - somewhat modified just now). This follows the guidelines at Wikipedia:Make technical articles accessible, specifically most accessible parts up front, add a concrete example, add a picture, and do not "dumb-down".

Once we address this basic issue I think the other issues will be easier. -- Rick Block (talk) 19:43, 29 December 2009 (UTC)

---

Overview

So, let's start at the very beginning...based on my analysis of the archives (*whew*), the positions stated here, and the current article lead, am I correct in understanding everyone agrees on defining the core Monty Hall problem as the one presented in Parade magazine in 1990 that reads:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

--K10wnsta (talk) 22:01, 1 January 2010 (UTC):

I'm not sure what you mean by "core". This is certainly a well known statement of the problem, but it is not very precise. What the the standard analysis is based on (per Barbeau) and how people generally interpret it (per Krauss and Wang) is consistent with the more explicit Krauss and Wang version from the "Problem" section of the article. In particular, the initial placement of the car is assumed to be random (and/or the player's initial choice is assumed to be random) and the host is constrained to always open a door deliberately revealing a goat, choose between two goats randomly, and always make the offer to switch. The effect of changing or omitting various of these assumptions is discussed in the "Variants" section. -- Rick Block (talk) 22:54, 1 January 2010 (UTC)

That is the most often quoted and the most notable statement but, as Rick says, it leaves a lot out. Martin Hogbin (talk) 22:57, 1 January 2010 (UTC)

I started a concept here taking the Parade version and K&W into account. If everyone agrees, we may proceed from there.Nijdam (talk) 12:30, 2 January 2010 (UTC)

Hello K10wnsta. There are several editors here keen to get on with improving this article. Are you still intending to mediate? Martin Hogbin (talk) 10:08, 4 January 2010 (UTC)

Yes, and I apologize for the delay. I have written and rewritten and deleted probably ten thousand words worth of questions, answers, and ideas to offer here and always end up backtracking and starting over because, honestly, you guys have covered every imaginable nuance and detail of the issue in past discussion here. It is not a decision I came to lightly, but I must wash my hands of this. This is an issue that I cannot help you to resolve.

Prior to stepping away and recommending formal mediation (actually, I would recommend some binding arbitration, but we'll follow procedure), I would like to present to you my own perspective (or a third opinion) on the state of the article (and this is boiled down from three lengthy paragraphs):

I was intrigued by the problem. Reading the article, I had the same reaction most people have when the problem is initially presented ('it must be a 50-50 chance'). The actual solution seemed outlandish. Once I read the explanation with the door diagrams, a light bulb went on and it made sense - it was better to switch. Much like the birthday problem, it's an intriguing solution that seems to defy logic. Once explained, it makes sense, and the novelty no longer exists. Everything else in the article is over-analysis, largely because it goes about solving variations of a problem that, once varied, lack the same novelty response that makes the Monty Hall problem notable to begin with.

Again, I'm sorry for the delay in posting this, but it was something I really didn't want to give up on. I wish I could offer more than just an opinion on the state of things, but you guys are so far out in left field in your analysis of this, I just can't wrap my head around it. Sorry I let you down.
--K10wnsta (talk) 01:04, 5 January 2010 (UTC)

Methods of numbering doors

(I welcome you all back to my screen. This article has improved a lot over the last year.)

Morgan et al. (1991) seem to assume that the doors are statically numbered, having the same numbers through repeated experiment. Vos Savant however writes in her column: "You pick a door, say #1, and the host opens another door, say #3". This may mean that after a door is picked, we (always) call it #1, while the opened door is (always) called #3. Such dynamic numbering can make it easier to discuss and calculate the given options. The consequences of the assumption of Morgan et al. are further explained in this article under "Probabilistic solution - 1991".

The Morgan paper classifies solution F5 as "incorrect because it does not use the information in the number of the door shown". This is only true assuming statical numbering. In this context it is questionable why Morgan et al. quote vos Savant wrongly, writing "You pick door No. 1, and the host opens No. 3". Heptalogos (talk) 14:11, 30 December 2009 (UTC)

The show the problem clearly refers to (Let's Make a Deal, hosted by Monty Hall) had doors with numbers on them. Here's a screenshot [5]. You could assume the doors are numberless and the numbers magically appear on them as they are used, but the question for editing purposes is what reliable sources say about the problem. Are you suggesting this "numberless door" interpretation is the predominant one used by reliable sources - or is this more like your own original research? If the latter, I'd suggest moving or continuing this thread at the #Arguments subpage. -- Rick Block (talk) 18:00, 30 December 2009 (UTC)

The Morgan paper is not about Monty Hall, but about a question in a column of vos Savant, starting with "Suppose you're on a game show". All exact information is, of course, in the paper, so no other sources are relevant. Heptalogos (talk) 19:44, 30 December 2009 (UTC)

So, again, are you talking about what reliable sources say (if so, references would be helpful), or something you've thought of on your own (if so, please use the #Arguments page)? -- Rick Block (talk) 19:56, 30 December 2009 (UTC)

The source I mention, "Morgan et al. (1991)", is probably the most argued source in this article. It is in the article reference list mentioned as: "Morgan, J. P., Chaganty, N. R., Dahiya, R. C., & Doviak, M. J. (1991). "Let's make a deal: The player's dilemma," American Statistician 45: 284-287." Heptalogos (talk) 20:11, 30 December 2009 (UTC)

If you're suggesting to move or continue discussion about the specific arguments used in the Morgan source, to or on the arguments subpage, then that's fine with me. But I'm doing more than that, namely introducing a new element to the global dilemma, which is the method of numbering doors. Heptalogos (talk) 20:43, 30 December 2009 (UTC)

I think the point that you are making is already covered by considering the player's initial choice to be random. In other words we can take it that either the Morgan paper refers 'only to the specific door numbers shown or that all the door numbers including the door opened by the host are examples only. Martin Hogbin (talk) 21:03, 30 December 2009 (UTC)

The Morgan paper is quite clear about the disctinction between conditional and unconditional. I quote: the unconditional problem, which may be stated as follows: "You will be offered the choice of three doors, and after you choose the host will open a different door, revealing a goat. What is the probability that you win if your strategy is to switch?" The distinction is made by opening a specific door, instead of "a different door". This is mentioned elsewhere in the paper several times. I agree that No. 3 is an example and might be No. 2 as well, but the paper assumes that there is an essential difference between "the open door" and "door No. x, which is open". To my opinion these are only labels which don't make any difference, unless of course one assumes that a specific door is labelled the same through repeated experiment. Heptalogos (talk) 21:40, 30 December 2009 (UTC)

Yes, they're clearly assuming distinguishable doors with persistent numbering. Is the topic you're introducing, specifically "the method of numbering doors", discussed in reliable sources or is this a topic you're introducing based on your own personal knowledge? Once again, only in the former case is this an appropriate topic for this page. If this is the case, please provide references to sources that discuss this topic. There are plenty of disagreements here without delving into original research. -- Rick Block (talk) 22:47, 30 December 2009 (UTC)

I want this article to explain how the conditional probability could actually differ from the overall probability (I refer to chapter "Probabilistic solution - 1991"), when the distinction between both is made by information (a door number) which seems to have no statistic dependency or influence on the requested probability. To my opinion, the average intelligent reader of this paradox, who has no mathematical skills, still doesn't understand the necessicity of using the relatively complex method of conditional solution. I agree that the discussion about the necessicity itself should preferably be held elsewhere, but an elementary explanation key in the article should be, I guess, in the idea of a static door position through repeated experiment, whatever it means. The meaning of that I would like to be explained. Heptalogos (talk) 23:45, 30 December 2009 (UTC)

I would actually prefer a combined solution section, like the one above (#Proposed unified solution section). It presents a conditional approach as an alternative, with a brief explanation of the difference between the conditional probability and the average probability, with a forward reference to the "Variants" section (at the moment called "Variants - Slightly Modified Problems"). Is this version more clear? -- Rick Block (talk) 01:02, 31 December 2009 (UTC)

I propose adding a link in external references

I propose adding an external link to http://www.opentradingsystem.com/quantNotes/Monty_Hall_problem_.html

The link in question contains derivation of solution in a general context developed on other examples. —Preceding unsigned comment added by Kaslanidi (talk • contribs) 20:27, 30 December 2009 (UTC)

I object, per WP:ELNO points 1, 4, and 11. - MrOllie (talk) 20:32, 30 December 2009 (UTC)

Yes, I Have A 'POV'.

My 'POV' is that this paradox twists peoples' brains a lot, just the way it is. Whatever 'is' means.

So a sequenced roll out of how the problem became published, then controversial twice would help the interested reader. What could make more sense then to describe the events roughly as they occurred, and beliefs/understandings changed, or maybe they didn't.

Let the reader decide for himself, or herself.

Yes, 'sequenced roll out' really means 'chronological'. Forgive me.

Pretty radical, eh? Just tell the story as the sources do, and let the reader draw his own conclusions. Whoda thunk it? Glkanter (talk) 20:35, 30 December 2009 (UTC)

I'm not sure I understand what you're suggesting. There is already a "history" section. Are you suggesting pitching the entire article and starting over with a strictly chronological accounting that would be sort of an expanded version of the "History" section? Or are you simply saying the same thing you said above as your position in the "Mediation" section, i.e. that you want to see 3 solution sections? -- Rick Block (talk) 01:37, 31 December 2009 (UTC)

Same thing. Or 1 Solution section with 3 sub-headings.Glkanter (talk) 02:02, 31 December 2009 (UTC)

BEST WISHES TO YOU ALL

And a fruitful start (continuation) in 2010! Nijdam (talk) 11:45, 31 December 2009 (UTC)

I would like to echo the last comment: Best wishes to all! And a fruitful start (continuation) in 2010. Gill110951 (talk) 19:36, 3 January 2010 (UTC)

What If Morgan Had Used A Different Variant?

Say, the 'forgetful' Monty?

Marilyn vos Savant says this is really a 'random' Monty, who might reveal a car.

I expand this to say, if it's random, then anyone, including the contestant could open the doors.

And if it's the contestant, then we're really talking about 'Deal Or No Deal'.

Does it makes sense to criticize the original solutions to the MHP based on an analysis of Deal or No Deal? Not in my book. Glkanter (talk) 17:21, 1 January 2010 (UTC)

If Monty *might* reveal a car nothing much is changed: the player always switches (only she should be sensible about which door to switch to). If Monty might *not open a door at all* then of course things do change, though under some conditions they don't. Game theory solves this case. If Monty might or might not open a door, and if he might reveal a goat or a car when he does (he does know where the car is), then the minimax solution is the very boring game: the car is hidden uniformly at random, and Monty never opens a door; the player chooses her door uniformly at random, and thereafter never switches. With those strategies the player is guaranteed at least a probability of 1/3 of winning the car; the quiz-team is guaranteed a probability of at most 1/3 of losing the car. So this solution is the saddle-point or Nash equilibrium. (von Neuman's theorem says that there certainly is a saddle-point). I think the solution is unique too: if the player would use any other strategy then the quiz-team could decrease their car-losing probability from 1/3, and if the quiz-team would use any other strategy then the player could increase her car-winning probability from 1/3. Gill110951 (talk) 19:46, 3 January 2010 (UTC)

I'm more interested in the idea that one can critique puzzle 'B', and find fault with puzzle 'A'. Which is what Morgan do, and every time I ask Rick to critique the simple proofs, much as I asked him about Huckleberry, he replies with a critique of a different puzzle. I don't get it. I think it's baseless. Glkanter (talk) 20:26, 3 January 2010 (UTC)

Is Morgan et al. a reliable source by Wikipedia standards? Does this article say If, regardless of the host's action, the player's strategy is to never switch, she will obviously will the car 1/3 of the time. Hence, the probability that she wins if she does switch is 2/3. ... F1's beauty as a false solution is that it is a true statement! It just does not solve the problem at hand.?

Is Grinstead and Snell a reliable source by Wikipedia standards? Does this book say This very simple analysis [as a preselected strategy, staying wins with probability 1/3 while switching wins with probability 2/3], though correct, does not quite solve the problem that Craig posed.

Is Gillman a reliable source by Wikipedia standards? Does this article say This is an elegant proof [vos Savant's solution], but it does not address the problem posed, in which the host has shown you a goat at #3.

Perhaps you don't understand or don't agree with what they're saying, but the beauty of Wikipedia is that it doesn't matter whether you understand it or agree with it so long as what the article says is NPOV and verifiable against a reliable source. We have 3 reliable sources here which all say nearly exactly the same thing. -- Rick Block (talk) 22:34, 3 January 2010 (UTC)

So, did you check the sources of the popular solution? They are quite contradictory. Heptalogos (talk) 23:17, 3 January 2010 (UTC)

Yes, I have checked. They present an unconditional solution without mentioning conditional probability as if the solution is responsive to the question that is asked. So, we have reliable sources that say one thing and other reliable sources that say the first bunch is not quite addressing the problem. I'm open to any reasonable suggestion for how to present this in an NPOV fashion, but not ignoring the second bunch of sources because some editors disagree with what they say. -- Rick Block (talk) 00:19, 4 January 2010 (UTC)

I'm very sorry, you are right. I lost the context because I sometimes find it hard to understand Glkanter. The article is quite good on the solutions, very NPOV (without irony). Now let's hope some scientist attacks Morgan, Grinstead and Gillman in a very irrelevant, but reliable manner. Heptalogos (talk) 20:52, 4 January 2010 (UTC)

Another Straw Man from Rick. Both sides go in the article. Why not chronologically? I've been saying this for a week. Your's and Morgan's POV not dominating the current article? Don't make me laugh. Now, why not answer for yourself, as a sentient being, what does "Suppose you're on a game show...' mean? Without hiding behind Wikipedia's policies. It's OK, we're on a talk page. Glkanter (talk) 01:16, 4 January 2010 (UTC)

Kind of ironic that you're complaining about straw men in a section titled "What If Morgan Had Used A Different Variant?", don't you think? I've asked you before, but where exactly do you see Morgan's POV dominating the article? As far as I can tell the only mention of this POV is in the "Probabilistic solution" section, the 4th paragraph in "Sources of confusion" and a paragraph in "Variants". -- Rick Block (talk) 02:53, 4 January 2010 (UTC)

All is right with the world. As we enter our 15th month of this argument, I disagree with you on the meanings of both 'Straw Man' and 'ironic'. Your POV? It's in every word except the intro and the Simple solution section. You just don't see it for some reason. Glkanter (talk) 06:19, 4 January 2010 (UTC)

And, of course, you avoided the question I asked you. Glkanter (talk) 06:20, 4 January 2010 (UTC)

What question is that? What does "assume you're on a game show" mean? I've answered this before. It provides a context for what is meant by "host" and "contestant" and "door". -- Rick Block (talk) 15:26, 4 January 2010 (UTC)

What is the Morgan scenario?

I have now shown that in order to get an answer (probability of winning by switching) of anything other than 2/3, Morgan have had to assume that we know that the producer places the car randomly, but we do not know that the host opens a legal door randomly. Is there anyone here who can justify that odd POV.? Martin Hogbin (talk) 10:12, 4 January 2010 (UTC)

Yes. There will be at least one editor who will attempt to justify that odd POV. Glkanter (talk) 13:10, 4 January 2010 (UTC)

It's not "Morgan's scenario", but Morgan's interpretation of vos Savant's scenario - perhaps "Morgan's vos Savant scenario" would be a better way to refer to it. It exactly matches the rules she sets up for the experiment she describes in her 3rd column, see [6]. I assume this is the "false simulation" they refer to in the introduction to their paper. The cups are labeled #1, #2, and #3. The host randomizes where the penny is placed. The contestant randomizes her pick. Then the host "purposely lifts up a losing cup from the two unchosen" (no mention of randomization in the case where the host can lift up either unchosen cup, even though both the initial placement and the player's pick are explicitly randomized). What is counted is overall success when not switching and overall success when switching, rather than success when not switching and success when switching for players who have picked cup #1 and have seen the host reveal what's under cup #3. This experiment is explicitly addressing the unconditional probability of winning by switching rather than the conditional probability - in a setup where they might actually be different (since the host is not required to randomize his choice of cup to lift up in the case where there is a choice). -- Rick Block (talk) 15:14, 4 January 2010 (UTC)

It really is unfair to try to blame vos Savant for failings in the Morgan paper. Sure Morgan mention vS at the start of their paper, they also mention the "prisoner's dilemma" (where the warden does secretly toss a coin), and Mosteller's' solution. Later on they state that vS took it that the host never reveals a car, and it is clearly this rule that they describe as the vos Savant scenario.

Regardless of what vos Savant or anyone else assumed, Morgan are under an obligation to firstly make consistent assumptions (for example that all unstated distributions are to be taken as random) and then to make clear the assumptions that they have made. They conspicuously fail in both of these respects.

Morgan claim to have 'an elegant solution that assumes no additional information', clearly referring to the Whitaker's original question, rather than vos Savant's interpretation. Their solution does not live up to this claim.

Finally, regardless of reasons or motives, Morgan do in fact consider the scenario that we know the producer places the car randomly but we do not know that the host chooses a legal door randomly. Their answer of 1/(1+q) is based on this scenario. This is not a reasonable or consistent assumption thus their answer of anything other than 2/3 is not valid. Martin Hogbin (talk) 16:11, 4 January 2010 (UTC)

Rick, you are still misrepresenting MvS's statements, and that is an example of how you inject your POV into everything you write. Please stop taking her statements out of context. "Anything else is a different question" refers to all of the assumptions she made in her approaches to the solution. That includes random car placement and random host selection (if needed), and excludes any dependence on Door #1/Door #3 that you think is included. Her shell game analogy did not number the shells, yet she said it was the same problem. As you yourself point out, the cup experiment does not mention picking cup #1 or lifting cup #3. You can't treat that part as an error; it, too, has to be part of any "exact match to the rules she sets up." So Morgan's interpretation does not qualify.

In the literature, there are two camps that do not agree with each other, and that never reconcile their differences (well; actually, MvS does - she said Morgan's is a different problem). Those that follow Morgan's "conditional problem" and those who agree with Seymann, that "the host is to be viewed as nothing more than an agent of chance who always opens a losing door, reveals a goat, and offers the contestant the opportunity to switch to the remaining, unselected door." Insisting that only the former group is correct is POV, and that is what I mean when I say you inject your POV. I will only stop saying it, when you stop doing it. Morgan's POV can be handled in the article; but it clearly is not the problem MvS intended. That fact is acknowledged in literature. So the article needs to first address the problem she said was intended, and then add the second opinion in as a variant, and clearly label it as a variant. That is the NPOV approach.

Martin, I firmly believe that Morgan never intended to introduce theirs as a "variant" problem, or to avoid making assumptions like the one about car placememt. All they ever say, is that one of the assumptions MvS made is not necessary to answer the question "should we switch?" They misspoke when they said "assumes no additional information," they quite clearly meant "assumes no unnecessary information," since they did make assumptions. And their answer to the Monty Hall Problem does not use the 1/(1+q) result, it only shows that no specific value is needed. It was an intellectual excersize only, and is not intended to be the MHP. So yes, it would be inconsistent to give an answer that includes q but not P(C₁), P(C₂), and P(C₃). My point here is that they don't - but they also fail to make it clear to their readers that they don't. JeffJor (talk) 17:14, 4 January 2010 (UTC)

Jeff, I agree, the Morgan paper is not entirely without interest or value. They show how, in a more general case, the host behaviour is important, firstly in never showing a car, then in choosing which door to open, but the player can never do worse by swapping. The problem is that they make such a bad job of what they do that it is hard to work out exactly what their main point is, except to criticise others.

My main point is that there is no justification for saying that in the MHP, with standard rules, the action of the host is important. There are only two logical and consistent ways to look at Whitaker's question. Take it as a real world question about the actual probabilities on hypothetical TV show, in which case it depends on so many factors that the answer is indeterminate, or take it as a mathematical puzzle, in which the normal mathematical puzzle assumptions are made, undefined distributions are taken as random etc. Anything else is, as you say, just an intellectual exercise. Martin Hogbin (talk) 18:11, 4 January 2010 (UTC)

I disagree on 1 point, Martin. "Suppose you're on a game show..." means the car placement and host choice, as far as the contestant is concerned, are random. This is true whether it's a hypothetical game show, or a mathematical puzzle. Because that is the host/contestant relationship on a game show. And it's every bit as much a premise of this math puzzle as '1 car and 2 goats' which is clearly stated. Because 'Suppose you're on a game show...' has also been clearly stated. Glkanter (talk) 18:44, 4 January 2010 (UTC)

It depends on the presumed state of knowledge of a contestant on the hypothetical show. Maybe the contestant has watched the show and discovered that the car is most often behind door 1. I do agree that a natural assumption would be that a contestant would have no knowledge of how the car might be placed or the host would choose but in real life this might not be the case. I am not seriously pushing the real life option, just stating that it is the only logical alternative to the 'puzzle' option. Martin Hogbin (talk) 20:01, 4 January 2010 (UTC)

Martin, this is not about "real life." It is a thought puzzle, only. No biases, or unrandom occurrences, can be assumed unless specifically stated. But this has nothing (directly) to do with "Suppose you are on a game show..." It has to do with its not being mentioned. You must assume any unmentioned options have to be random between the possibilities (and so this is another reason the conditional solution can't be used.) JeffJor (talk) 20:32, 4 January 2010 (UTC)

Jeff you are the hardest person in the world to agree with sometimes. As I said to Glkanter, the real world scenario is the other consistent option, but I agree that the real one in the 'puzzle' option. Martin Hogbin (talk) 20:40, 4 January 2010 (UTC)

Martin, you have a problem because you don't acknowledge the fact that it is your argument, not your conclusion, that I disagree with. There is no supportable definition for what "suppose you are on a game show" means, so it is pointless to try to argue for a meaning behind it. There also is no justification for trying to place the problem in a real-world setting, which is one of the problems with Morgan. (Just like "What is the probability that the woman I met yesterday, who has two children, has two boys?" The real-world answer is 100%, because she does have two boys. The intent of the question, as a puzzle, is 25%; and the real-world scenario is completely irrelevant.) So I view any arguments based on eithar as being counter-productive. JeffJor (talk) 17:31, 6 January 2010 (UTC)

Jeff - I'm merely suggesting where Morgan et al. got the "odd" scenario from. MvS explicitly said lots of things, but never (as far as I know) explicitly said anything about how the host chooses when given the chance (at least not before the Morgan et al. paper was published). This is NOT "my" POV, but Morgan's POV (that I seem to be the only one representing here). I'm FINE with treating this specific scenario as a variant (it's already been moved to the variant section), but I don't think it means that a conditional solution must also be deferred to a variant or that a discussion of whether the question refers to the unconditional probability or the conditional probability must be deferred to a variant. The unconditional and conditional probability for the fully explicit version (including "host picks randomly if given the chance") are the same - we all agree about this - but I think clarifying that these are different questions and which approach addresses which question should be part of the initial "Solution" section. -- Rick Block (talk) 19:12, 4 January 2010 (UTC)

Rick - I'm not saying that your agreeing with Morgan, per se, is POV. I'm saying that disagreeing with MvS on the same subject, where she disagrees with Morgan, is POV. You said "[Morgan's interpretation] exactly matches the rules [Marilyn vos Savant] sets up for the experiment she describes in her 3rd column." It does not - why do you ignore that part of what I said? It exactly matches what Morgan said her set of rules was, a set she explicitly denied was her intent. There are two parts to that difference, and it requires both of them to make Morgan's interpretation applicable to anything: There is the question about whether Door numbers are important (they aren't, and she explicitly made that clear because she does not use the numbers in her two analogies), and there is the question about how the host treats door numbers if they are important (which MvS doesn't mention, but doesn't need to: as per Seymann, the host is only an AGENT OF CHANCE and so everything he does must be goverened by chance alone. That is the statement you are missing. But even if that is not accepted, since the door numbers are not important, no such bias can be used. You yourself pointed that out, because her experiment was "explicitly addressing the unconditional probability of winning by switching rather than the conditional probability." Those are what her rules are, according to her.)

To say there is a match requires that you ignore MvS's comments and accept only Morgan's. We simply have to beleive MvS's statements of what her intent was, over Morgan's. That's what makes their treatment a variant, and what makes disagreeing with her "set of rules" POV even if you find sources for support. Plus, you misinterpret Morgan (I still must be speaking in cat whan I say this): They do not present a solution to the MHP that includes q. They show that if the MHP is CHANGED (they don't call it a change, but MvS does, so we have to treat it as one to be NPOV), then you get the same answer ("switch") no matter what q is. But they ignore placement bias the exact same way MvS does, because it does affect the answer, and is part of being an "agnet of chance."

There is no justification for saying the host's preferences for opening one door over another matters, because the MHP is about the strategy, not the doors. Any mention of it belongs with the variants, and even then we have to say that you can't use it unless you know it. JeffJor (talk) 20:25, 4 January 2010 (UTC)

Jeff - How do the rules of Morgan's vos Savant scenario not match the experiment she described? As far as I can tell, the difference is whether you're ignoring the conditional question and intending to answer the unconditional question (like vos Savant does) or whether you understand there may be a difference and are intending to answer the conditional question (like Morgan et al. says is what the question asks). Which specific comments of MvS's (from her columns) did they ignore? It sounds like you're claiming the quote "Anything else is a different problem" applies to anything you'd like it to apply to. Here's the full quote:

Rick - I can keep repeating this as often as you ignore it: Morgan assumes that the door numbers were intended to be used as part of the problem, and not meant as examples. MvS does not. That is, Morgan addresses what you call "the conditional proeblem," which is part of what MvS calls "a different problem." As I said twice yesterday, this is clear because the two analogies she uses do not use those door numbers in the solution, not even the one (and only one) that includes them in the description. So how can you ask this question? Her experiment that does not use door numbers, and that you said "exactly matches" a treatment that does. So I'm not "ignoring" the conditional problem, I'm saying (1) It isn't there to be ignored, (2) teh conclusion that it is comes from a misreading of the problem (K&W say the door numbers are sematically just examples) (3) MvS has denied it is intended, which allows us to ignore it and still be NPOV (4) Seymann acknowledges it is not how the problem shoud be read, and (5) The vast majority of sources that address what they call the MHP, especially in popular literature where the controversy exists, do not consider it at all. Selvin, Savant, Gardner, Tierney, Delvin, Mlodinow, and others all either ignore door numbers, or uses them as examples and treat them as though they represent "without loss of generality" selections. JeffJor (talk) 17:25, 5 January 2010 (UTC)

Morgan et al. assume the door numbers are persistent and the problem pertains to a player who has initially selected a specific door and has seen the host open another specific door. They use the example case of door 1 and door 3 as representative of any other (equivalent) case. Selvin (2nd letter), Morgan, Gillman, Grinstead and Snell, Chun, Falk, and others all approach the problem this way using this case "without loss of generality". -- Rick Block (talk) 19:48, 5 January 2010 (UTC)

Only partially right, Rick. Not all use the phrase "without loss of generality." Those that do, are acknowledging that they are using single cases to represent all of the symmetric cases. Those that never consider "host strategies" other than random selection - like Selvin in what he calls an alternate solution - are implicitly doing the same thing. It is the insistence that the problem [i]must[/i] be solved with conditional problility AND that this solution must consider p!=q that we object to. Once you remove that second possibility, there is no need to use specific doors. You can change "Door #1" to "the chosen door," "Door #3" to "the opened door," and "Door #3" to "the remaining door." There is no way apply the parameters p and q this way. Doing so removes a level of complication that obfuscates the MHP to the casual reader, and so makes the article more readable. JeffJor (talk) 17:22, 6 January 2010 (UTC)

So let's look at it again, remembering that the original answer defines certain conditions, the most significant of which is that the host always opens a losing door on purpose. (There's no way he can always open a losing door by chance!) Anything else is a different question.

You're telling me you're absolutely sure "anything else" here does not refer specifically to the host opening a losing door on purpose but to all the "certain conditions" that she hasn't enumerated (and, so, anything she might need to justify her solution is included). Furthermore, you're telling me that in spite of explicitly labeling the cups she never meant the labels to mean anything (!?), and in spite of explicitly randomizing the initial distribution of the penny under the cups as well as the contestant's initial choice but saying nothing about the host's choice when the host has a choice she clearly meant the host to choose randomly as well (?).

What is "anything else" comparing? Questions. What is the subject of the paragraph? Conditions that are defined for her question, by her answers. "Anything else" means anything other than the conditions she describes - those stated in her original problem OR implied by her solution. And it is quite clear in "opens a losing door" is just one example of a condition she means, and yes it is quite clear there are others. So absolutely, positively, can't mean just that one specific condition. JeffJor (talk) 17:25, 5 January 2010 (UTC)

I think we both know she simply wasn't thinking of the conditional case at all - which is precisely what Morgan et al. criticize her for since in their view the question is clearly what is the chance of winning by switching in a specific case (such as the player has picked door 1 and the host has opened door 3). The chance is the same as the unconditional chance only in "certain conditions" one of which is that the host choose randomly when able to choose - or, less realistically, you can't tell the difference between the doors - or, more pedantically, you're restricting the solution to the player's SoK and assuming the player has no way to know about a host preference (essentially a sophisticated way of saying you can't tell the difference between the doors). You're saying MvS clearly understood this and clearly meant this to be one of the conditions of the problem. Fine. You're certainly entitled to your opinion, but since she never explicitly mentioned it in her columns (or, BTW, even in her rejoinder to Morgan et al.) it seems like there's a pretty good argument that she overlooked this condition. It was one of the first things Selvin mentioned in his second letter about the problem in response to the letters he got. It's not a "throwaway" detail. What I'm saying is that this article should not treat it as a throwaway detail either.

And how is "not thinking of" different from "not intending?" JeffJor (talk) 17:25, 5 January 2010 (UTC)

As far as my POV, what I'm saying is that there is a difference between a solution that inherently addresses only the unconditional probability and a solution that is able to address the probability in a specific case. I would like BOTH to be presented, as equally valid solutions to the fully specified, symmetric, problem (where the answer is the same). Based on how violently you're objecting to this are you arguing that a conditional solution is somehow wrong? -- Rick Block (talk) 01:07, 5 January 2010 (UTC)

There is no "specific case." It is an example. Here's another one: A woman I met at random yesterday has two children. What is the probability she has two boys? Answer, for the specific case: 100%. Answer clearly intended by the question: 1/4. It's a puzzle that uses an example to describe the random process. The example is not intended, and never is in such questions unless specifically included. And it has to be so, because probabilities do not apply to specific cases. They only apply to random processes. JeffJor (talk) 17:25, 5 January 2010 (UTC)

Since I can enumerate the specific cases (player picks door 1 and host opens door 2, player picks door 1 and host opens door 3, etc.) your claim that there is no specific case seems rather curious. Bottom line, you're saying "yes" a conditional solution is wrong? -- Rick Block (talk) 19:48, 5 January 2010 (UTC)

And once again, you insist on ignoring the point so that you can justify including Morgan. The numbers are not a part of the problem, they are only examples used to illustrate the problem. Stop me if you've heard this before: "Say," when used as an adverb like that, means "for example." The problem statement without examples is "Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door ... and the host, who knows what's behind the doors, opens another door ... which has a goat. ... Is it to your advantage to switch your choice of doors?" The parts I removed are simply not part of the question that is being asked. Period. We also know MvS intended it that way, because the statement as I just worded it is the only statement that is equivalent to Marilyn's two experiments. The only source that addresses why we should, or shouldn't, use the so-called "conditional problem" is K&W. All others merely assume one or the other (some implicitly and some explicitly, but still an assumption) without justifying why. And when they present that argument, K&W say the door numbers are not semantically part of the question. So by the Wikipedia guidelines, the only problem we can consider "the" MHP is the unconditional one. Morgan's treatment of it does not address her problem, because they changed the wording in the quote to insert the door numbers into the actual problem. So we cannot use Morgan as a source that addresses our main problem, and any solution they depends on specific door numbers must be relegated to the section on the variant they created. (Note that Selvin's conditionl solution does not depend on the door numbers, as it sets all probabilities by the assumption of uniformity. I've always agreed it can be used as a solution, but not with q != 1/2. And it doesn't help explain the controversy.) JeffJor (talk) 16:41, 7 January 2010 (UTC)

Let's continue this during mediation if you don't mind. -- Rick Block (talk) 19:41, 7 January 2010 (UTC)

JeffJor, I'm with you on this 100%. So, living with the requirement that since they're published, Morgan and its ilk must be included in the article, how would you apply your argument to the article? Bear in mind, imho, the conclusion that 'Morgan's paper does not address the MHP' is, unfortunately, OR. Unless you have a source? Seymann just couldn't quite say it. Glkanter (talk) 18:03, 7 January 2010 (UTC)

Formal mediation

The informal mediator bailed, so the next step is formal mediation. The guts of the request are the sections I've put up at User:Rick Block/DraftMed. Before filing the request, I'd suggest anyone who's interested take a look. There are separate sections for issues the "filer" is asking to be mediated as opposed to issues other parties want mediated (feel free to add whatever you'd like). I don't care who actually files it (it really shouldn't matter), but have filled this out as if I'll be the one doing the filing. If anyone strongly objects to this we can rearrange things so someone else will be listed as the "filer" (but then whoever this is will have to actually file it at Wikipedia:Requests_for_mediation/File, and notify the involved parties). -- Rick Block (talk) 02:48, 5 January 2010 (UTC)

Unlike informal mediation, formal mediation will be rejected unless all parties named as involved parties agree to mediation. Please indicate here whether you consider yourself to be an involved party, and whether you're willing to participate in mediation. For more on what is involved, please see Wikipedia:Mediation Committee/Policy. If you consider yourself to be an involved party and refuse to participate, the mediation committee will refuse to take the case. At a minimum, I consider myself, Glkanter, Martin Hogbin, and JeffJor to be "involved parties", although Nijdam, and Kmhkmh have been fairly involved in the past as well. Naming more, particularly anyone who is not willing to participate in the process is extremely counterproductive. -- Rick Block (talk) 05:22, 5 January 2010 (UTC)

Well, it's a 'chicken or the egg' kind of thing. Just because you listed someone doesn't mean he will participate/accept the results. I tried to do a 'pre-agree' and after a few days passed, you said that wasn't how it works. The people I added have been participants in the last month or two, and should be offered the chance to be involved. Almost all of them were either part of the consensus or agreed to take part in the formal mediation when I asked.

But I agree, we don't want a named person bringing the formal mediation to a halt. Has Nijdam indicated his willingness to participate to you? Glkanter (talk) 13:08, 5 January 2010 (UTC)

Nijdam has not indicated anything to me. Any pre-agreement is not official. I've trimmed the list back to those who previously indicated a willingness to participate, plus Nijdam and Kmhkmh (I'll ask them both directly). If neither of them indicate they're willing we should talk about how to proceed. -- Rick Block (talk) 14:37, 5 January 2010 (UTC)

I'm willing to take part in formal mediation. Nijdam (talk) 16:43, 11 January 2010 (UTC)

I have posted an edit at Seems selective regarding the invitee list. Glkanter (talk) 16:21, 6 January 2010 (UTC)

I cannot claim to be involved. Although I wanted to participate, lately I have found myself so busy with other things that I have not had the time to dedicate to trying to help with this thorny problem. Good luck and good grace to all, though.--Father Goose (talk) 08:08, 5 January 2010 (UTC)

I'm not sure (and it perhaps depends on the mediator and/or the case), but I think even if you're not listed as an involved party you can generally participate. -- Rick Block (talk) 14:37, 5 January 2010 (UTC)

I would like to participate. Heptalogos (talk) 20:03, 5 January 2010 (UTC)

Do we need it?

Despite continuing discussion and some disagreement, I think there has been a move towards increased understanding between all the parties involved. We should also all congratulate ourselves on keeping the discussions civil and avoiding edit warring.

Now is the time to move on and start improving the article. Some of us have written down our objectives for the article for the mediator and they do not look that far apart. With goodwill and some concessions on both sides we should be able to make considerable progress. We all need to give a little and be prepared to drop some of the finer points of our arguments. For example, I believe that there is no rule telling us that the K&W formulation must be treated conditionally (and I am happy to continue this discussion on the 'arguments' page) however, I am prepared to accept a statement along the lines of, 'strictly speaking this problem is one of conditional probability', if appropriately placed.

I appreciate that I am not a neutral party in all this but I am going to start a new section below, which I will call 'Self-mediation', just to see if we can find things that we agree on. Martin Hogbin (talk) 09:59, 5 January 2010 (UTC)

Self-mediation

This is a section where I hope to find as many things that we can all agree on. Can editors please indicate their agreement or otherwise below. I will add just two items to start, which I hope there will be fairly general agreement on.

Make better use of the two talk pages

This is just a matter of the mechanics of our discussion. This talk page should be reserved for discussion of proposed changes to the article: the general approach and format, what to say, where to put things, what diagrams to have etc. Discussion of the rights and wrongs of different sources, what is conditional and what is not, and other philosophical and mathematical issue around the subject should take place on the arguments page. It is important that this division is voluntary with only the gentlest of reminders to other editors to take their points elsewhere, if needed. Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

Agree

Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

Except I don't see why we need to be particularly gentle about it. Rick Block (talk) 16:10, 5 January 2010 (UTC)

Demanding people take their discussions elsewhere does not work and creates ill feeling. Here is the deal as I see it. Everyone agrees to use the two pages properly and engage in discussion on both pages. This means that those who want to keep the article as it is must engage in discussion about the underlying issues on the arguments page, otherwise those that do want change will bring those arguments here. Martin Hogbin (talk) 16:58, 5 January 2010 (UTC)

Except both pages are too long, and I find them hard to work with becaseu of that. JeffJor (talk) 16:38, 5 January 2010 (UTC)

The answer to this is archiving, if somebody knows how to do that. Martin Hogbin (talk) 16:58, 5 January 2010 (UTC)

Have essentially two sections

I think nearly everyone agrees that we should have two sections. In one section we should have the simple non-conditional solution (I think that non-conditional is a useful term in this discussion, which I use to mean not specifically mentioning or discussing conditionality, but not necessarily because the problem is agreed to be unconditional. Maybe the issue is being initially glossed over, in the interests of simplicity and clarity). In the second section we can mention the conditional nature of the problem and other variants and complications.

I am not yet talking about exactly what should go in each section, or what they should be called. I am just trying to get agreement to having a starting section that treats the problem simply, as we now have. Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

Agree

Martin Hogbin (talk) 10:16, 5 January 2010 (UTC)

The "conditional problem" - i.e., the one that uses Door #1/Door #3 - is a variant that definitely does not belong in the main section. Not only becasue it does not address the actual MHP, but because it does not help the uneducated reader to understand why the unintitive answer is correct. It only confuses him. It is NPOV to do it this way, because it separates the sources that treat different problems into sections that handle their own problems, rather than assuming the sources that handle the originally-intended problem are somehow wrong about what the problem they presented is. JeffJor (talk) 16:38, 5 January 2010 (UTC)

Disagree

I agree the initial section should focus on the fully symmetric problem, but strongly disagree about deferring a conditional probability solution to a subsequent section. IMO, this would not be NPOV. -- Rick Block (talk) 16:13, 5 January 2010 (UTC)

This is roughly chronological order of the sources. None of the sources before Morgan mentions conditional probability, why should we? My main aim (and that of may others I believe) in the first section is to keep it simple. I personally would not object to a footnote stating things might be a bit more complicated. Martin Hogbin (talk) 17:03, 5 January 2010 (UTC)

"None of the sources before Morgan mentions conditional probability"? This is absolutely false. Selvin's second letter [7] has a solution using conditional probability. The MHP was a well-known conditional probability problem in academia years before vos Savant's column. -- Rick Block (talk) 19:16, 5 January 2010 (UTC)

Yes, you are quite right, I was persuaded by the arrogance of the Morgan paper that they had discovered conditional probability. Selvin's second letter does indeed consider the probability with which the host chooses a given door. He, naturally, takes this to be 1/2 (as has already stated that the host will choose randomly when he has a legal choice) and proceeds, without fuss to solve the problem. In the light of this it is hard to see what the Morgan paper adds to the story.

Even so, this is not what I would like to see at the start of this article. I think we need to have a balance between what some see as mathematical correctness and simplicity, so that we can fulfill the basic function of WP of informing our readers. Let me make a proposal below, it is similar to that on Nijdam's development page. Martin Hogbin (talk) 11:34, 6 January 2010 (UTC)

Somewhere in between

Too soon the article is getting complex. The Whitaker question however seems to be most famous, but other well known examples from reliable sources are welcome. My main suggestion would be to use the information which is already in the article, but reshape it:

1. Introduction. (Until "When the above statement". Move the last two paragraphs to the "History" chapter.)
2. Popular solution
3. Conditional solution
4. Aids to understanding
5. History (general)
---similar problems
---Monty Hall
---American Statistician
---Parade
6. Arguments and methods (detailed)
---Conditional or not
---Variants
---Bayesian analysis
7. Links and references
Heptalogos (talk) 21:47, 5 January 2010 (UTC)

Discussion and proposals aimed at reaching a compromise on this subject

This section is intended for discussion of what editors would like to see as the first solution.

I would like to see this as the first solution in the article, with pretty pictures, of course. I also would accept a footnote of some kind to indicate that some people regard this solution as incomplete, exact wording to be negotiated.

You choose a goat		You choose a goat		You choose a car
The host opens a door to reveal a goat		The host opens a door to reveal a goat		The host opens a door to reveal a goat
You Stick	You Swap	You Stick	You Swap	You Stick	You Swap
You get a Goat	You get a Car	You get a Goat	You get a Car	You get a Car	You get a Goat

Rick, could you accept this? Nijdam? Martin Hogbin (talk) 11:47, 6 January 2010 (UTC)

I'm not Rick or Nijdam. I have stated at least twice that the only appropriate way to 'major edit' the article is to start with the current version. That way all adds/deletes/modifies are clearly discernible with a true audit trail. Is this obtuse to anyone? Do I need to rephrase that sentence for clarity? Do you catch my drift? Glkanter (talk) 12:11, 6 January 2010 (UTC)

My suggestion above is not suitable for immediate inclusion in the article because it needs pretty pictures. Everything done on WP is recorded so any agreements made here can be later transferred to the article with an 'audit trail' as you have put it the past. Do you like the suggestion above (with your choice of footnote, including none)? Martin Hogbin (talk) 13:51, 6 January 2010 (UTC)

And the footnote infers that 'Probability' is the only discipline available to solve the puzzle. That is false, and I will not support it's inclusion with the 'probability/logic solutions'. Unless you want to go to 4 distinct solutions in chrono order: The one above from 1975 (with footnote), Selvin's indifferent conditional from 1975, vos Savants probability/logic solution from 1990, and Morgan's non-solution from 1991. Glkanter (talk) 12:46, 6 January 2010 (UTC)

Would you be happy with a different footnote? If so what? Would you like to see the above solution with no footnote? Martin Hogbin (talk) 13:51, 6 January 2010 (UTC)

As an alternative, I suggest again a unified solution section, more or less like #Proposed unified solution section. The first part of this is (I think) pretty much exactly like what you're suggesting. But then instead of a footnote it continues with a conditional solution of the symmetric problem presented as an alternative. Maybe this will be the meat of the mediation, but I don't see how deferring a conditional solution to a later section rather than including one at this point is anything other than POV favoritism. The difference is only one screenful of text and figures, basically one paragraph. -- Rick Block (talk) 14:51, 6 January 2010 (UTC)

Here's another word Rick and I disagree on the meaning of: 'compromise'. Rick thinks (as per his edit summary) that going from 2 separate solution sections (as the article has today) to 1, is a compromise with the guy(s) who want 3 or 4. Another thing we disagree on is that chronological order has a POV. Maybe we should somehow have all the solutions typed on top of each other? To be fair, of course. Glkanter (talk) 15:13, 6 January 2010 (UTC)

If that's going to be your attitude then I see no point in continuing this discussion until we have a mediator. -- Rick Block (talk) 15:21, 6 January 2010 (UTC)

That's not an attitude, it's a statement of fact. I agree, you should stop trying to change the article in opposition to what the consensus wants. I've been trying to move us to formal mediation for weeks now. Glkanter (talk) 15:26, 6 January 2010 (UTC)

Rick, as you say, my proposed diagram (which was taken from 'The Curious Incident of the Dog...') is quite similar to yours but it does not have door numbers which, according to K&W, only confuse people. The footnote has the advantage of allowing us to present a clear diagram, which most people can actually understand, but still be correct. I think you have forgotten how difficult this problem is for most people when they first see it. We need to do all that we can to make the problem and solution simple, at least to start with. The main point of the problem is that the answer is 2/3 and not 1/2. We must get this across first.

I do not think that starting simply and then going into more detail can be regarded as POV. It is how most good text books work. Can we leave what happens after this diagram for the moment. Would you accept the diagram, with an appropriate footnote?

Glkanter, do you like my proposed diagram at all? Would you be happy for the article to start with this?

Finally, I do not think that formal mediation will achieve anything more than we are doing here. Everyone needs to compromise a little. Martin Hogbin (talk) 16:40, 6 January 2010 (UTC)

If the diagram represents the sources accurately, what else is there to say?

OK. Lets compromise. 1st question: Is the contestant ever aware of a host bias? How? Why? 2nd question: How many Solution sections? In what order? 3rd: What about the SoK problem in the Variants - Slightly Modified Problems section? 4th: Other than as part of Morgan's solution, will the probability/logic solutions be describes as 'false'? Will there be a statement that Morgan's view is not universal, more likely a minority opinion?

I think we need the Formal Mediation so that we can go to arbitration on ownership and filibuster issues. Otherwise, the consensus will continue to be improperly restricted from improving the article. Glkanter (talk) 16:55, 6 January 2010 (UTC)

As far as I can see my simple diagram meets all your requirements. Can you confirm that you like it and would be happy for the article to start with it? If not, I am wasting my time with it. Martin Hogbin (talk) 17:03, 6 January 2010 (UTC)

If you feel this would improve the existing article, I encourage you to make such an edit. If you are asking my opinion, I cannot render it out of the context of the existing article. It's a Featured Article. Why would anybody start over at ground zero, rather than add/delete/modify the existing article, or a copy? I've said this countless times, and you guys all just set up sandboxes all over the place. I take no responsibility for how anybody spends their time here, other than for myself. Glkanter (talk) 17:16, 6 January 2010 (UTC)

You thanked me for my support below, how about some from you now. Before I spend my time creating pictures and uploading them, I want to be reasonably confident that I am not wasting my time. I am not starting at ground zero, most of what is currently in the article can stay as far as I am concerned. I just want to start the article with a simple, convincing solution that shows that the player has a 2/3 chance of winning by swapping. This is what is missing, in my view. If I added such a diagram and solution, would you accept it? Martin Hogbin (talk) 17:52, 6 January 2010 (UTC)

Did I?

If I've learned anything from Wikipedia, it's that nothing can be 'assumed'. Until your mods are in the article, or a copy, I can only assume where you're putting it, what else you're changing, etc. And if I do that, then I haven't learned anything after all. Oh, and I don't agree with a footnote, or any other disclaimer. Until Morgan's direct criticism in Morgan's solution section. Glkanter (talk) 20:06, 6 January 2010 (UTC)

I guess I have to leave you to do things your way then. I was trying to reach some kind of consensus here but if you want to try, mediation, arbitration, edit warring, or whatever then go ahead. 86.132.191.65 (talk) 20:23, 6 January 2010 (UTC)

I think your table is quite clear, but I don't think it's easier to understand than the simple pictures in the Popular solution section. Actually I guess it's about the same as the first big picture. What's really different? Heptalogos (talk) 22:25, 7 January 2010 (UTC)

Interesting division in Wikipedia policy: Text - no OR; Images - OR is OK. Glkanter (talk) 22:49, 7 January 2010 (UTC)

Maybe The Host Has A Bias Towards Pretty Women?

So, by watching, you realize he nods his head at where the car is. Now the female contestant has a 100% likelihood of selecting the car.

This is equivalent to Morgan's argument about a left-most door bias. It's published, but pretty darn stupid.

There is no contestant, or viewer, awareness of a host bias on a game show. And the puzzle begins, 'Suppose you're on a game show...' Glkanter (talk) 17:20, 5 January 2010 (UTC)

Equivalent, except your scenario is NOT published in a well known peer reviewed statistics journal. And, in the extreme, if it were published (and there were multiple confirming sources) we should include it.

These little sections you keep adding that suggest no specific change to the article at best belong at /Arguments. Please stop posting them here. -- Rick Block (talk) 19:23, 5 January 2010 (UTC)

Glkanter's point, which I agree might be better in the argument page, is that even in a real-life scenario the player is unlikely to know much about the host's door choice and would therefore be reasonably expected to treat it as random. As this is, in fact, a mathematical puzzle, as the article makes clear at the start, it would be perfectly normal to take an unknown initial distribution as uniform. This makes the conditional answer exactly equal to the unconditional answer and the issue of conditionality somewhat irrelevant to explaining to a typical reader of this article why the answer is 2/3 and not 1/2. This is the improvement to the article that many of us here want. Martin Hogbin (talk) 23:51, 5 January 2010 (UTC)

Thanks for the support? My point is that this Pretty Woman variant is just as likely as the left-most door variant that Morgan (or Rick?, I've lost track and interest) uses to stigmatize the probability/logic solutions. They're both made from whole cloth. Mine is just less opaque in it's ridiculousness. I would not strike the keys of my keyboard to discuss the initial distribution. Although, I have spent 15 months arguing over a host bias. Glkanter (talk) 06:17, 6 January 2010 (UTC)

What is the argument in support of reporting Morgan's solution prior to the others'?

Why should Morgan's solution 'jump the line' over the other solutions, which were published earlier? It's no 'better' than any other. That would be a NPOV violation. Glkanter (talk) 16:37, 6 January 2010 (UTC)

Where are you getting the notion that anyone is arguing Morgan's solution should be reported prior to any others? Is there a change to the article you're suggesting here, or is this actually a response to something else? -- Rick Block (talk) 19:48, 7 January 2010 (UTC)

LOLZ! We need more humor in all these dry discussions. Thanks, Rick! Glkanter (talk) 03:39, 8 January 2010 (UTC)

Recent changes and discussions (early Jamuary 2010)

changes

I noticed that the article has changed quite a bit and not all for good.

good

• the current introduction looks good to me it thankfully stays away from Kraus&Wang and the unconditional vs conditional issue. But just state the problem in the parade version which made it famous

not good

• However, this is not the only mathematically explicit version of the problem. Were the names of the doors (the numbers 1, 2, and 3) fixed in advance (painted as huge numerals on each door), or are we naming the doors retrospectively: you choose a door and we call that door 1; then Monty Hall opens a door and we call that door 3; we then give the remaining door the name door 2? This latter appears to have been the intent of Marilyn vos Savant herself. <--- What's that supposed to be? Please no personal speculation of what the problem might be. And in the same manner no (unsourced) speculation of what vos Savant, Morgan or whoever might have had in mind. Stick to summarize what they've actually written.

Source: MvS site. Part of the actual problem statement: "the host opens another door, say #3". "Say" reasonably meaning to give it a random name out of three. This enables the host to say, in the particular event: "Do you want to pick door #2?", also quoted from the statement.

The first similar example described by MvS uses three shells. They are not numbered, reasonably because the chosen one is identified by a finger on top of it, and the other two similarly need no identification other than 'empty or not'.

The second example presents all six possibilities, including openings of door 2, which are counted as valid outcomes. This is probably the most explicitly convincing one.

The third example uses three playing cards in repeated experiment. The cards can't be numbered at all, because the numbers would reveal their value after a few times. This is probably the most implicitly convincing example.

The last example is the experiment actually performed. This one is trying to cover randomness by throwing dices. Three cups are numbered, in reference to the only valid outcomes of the dices. Again, both cups no. 2 and 3 may be lifted and are counted as valid outcomes.

So, it can be reasonably understood that the intent of MvS was not to fix numbers to doors, but rather to identify any possible situation at a certain moment. Heptalogos (talk) 13:11, 9 January 2010 (UTC)

Marilyn herself raised the fact that she was misquoted by Morgan: [8], creating early misimpressions. She accuses Morgan of purposely focussing on semantic issues. She further writes that no additional stated conditions appeared important to a general comprehension of the problem because circumstances in default are reasonably considered random. And finally she states that 'we' (herself and Whitaker?) published no significant reason to view the host as anything more than an agent of chance who always opens a losing door.

Morgan answered that they consider Whitaker's question as an original question, which makes any comment by MvS irrelevant. I don't know if MvS replied to that again, but she ends her letter with the phrase "I have given up on getting the facts across properly and have decided simply to sit back and amuse myself with the reading of it all".

They both make sense and I think this is another example of our need to take distance from opinion, taste and ethics, and present the issues as they arise, anywhere relevant and reliable. Heptalogos (talk) 22:21, 9 January 2010 (UTC)

• Popular solution - 1975. <---Excuse me? None of the sources/descriptions in this section is from 1975 but they are from the 90s onward. Furthermore Selvin (which is the supposed 1975 reference) published a unconditional (=popular) and a conditional solution in 1975. Conclusion this section header complete nonsense.
• Probabilistic solution - 1991. <--- Similarly off as the other section title. All solutions are "probabilistic" if they compute probabilities and use probability theory. That's the case for Gardner, Selvin and later treatments (including that partially that of vos Savant herself). There is also no unconditional vs. conditional difference between 1975 and 1991 if the section header is supposed to allude to that. The only thing that was "new" in 1991 was a generalization of the conditional solution to model different host behaviours.

discussion

Much of the discussion still evolves around "What the real MHP is (according to us)", "What the appropriate or true solution has to look like (according to us)", "What vos Savant thinks the problem means (according to us)", "What Morgan thinks the problem means (according to us)", etc.. While this can be an interesting discussion in its own merit it is largely pointless for the article. For the article we have to provide an accurate/representative summary of he how the problem was defined/solved/treated in reputable literature and that's it. It's not up to us to "decide" whether Morgan or vos Savant or whoever was ultimately "right" or did solve the "real" MHP while the rest was doing something else. If all participants would stick to summarizing all reputable literature in a representative and readable fashion as a goal and stay away from cherry picking sources and pushing their personal view of the problem much of disagreements would vanish.--Kmhkmh (talk) 01:47, 8 January 2010 (UTC)

So, what should the Solutions heading read for the first source that calls the Selvin/vos Savant solutions 'false'? Who gets the credit? What year did that happen? Some long-standing editors of the article seem to think that's a significant point in the history of the puzzle. Do you agree? Glkanter (talk) 22:47, 8 January 2010 (UTC)

You need to decide whether you want to have the chapters being organized by content or chronology. If want to order them by content, then as explained above the current section headers make no sense. If you want to order them chronologically then the headers should be something like 1975 _ Selvin when Selvin posed & solved the problem and coined the term MHP. And 1990 - Parade/Whitaker/vos Savant when the problem became widely known and the "controversy" started. I don't see any particular importance of Morgan in the time line here. He was just the possibly first of string of academic and math publications that followed after the parade affair. The problem with chronological sections however is that you cannot separate the conditional from the unconditional solution (since both are around in 1975). Furthermore we have a chronological overview in the history section anyhow. So if we organize by content the section headers could be something like simple/popular/unconditional solution (essentially with the current content) and conditional solution/detailed mathematical analysis (partially with the current content (conditional solution)m but possibly also the bayesian section and the variants. The header detailed mathematical analysis might also indicate to readers, that people just looking for simple and sufficient explanation do not have to bother, however people interested in various other perspectives or a more "advanced" treatment of the problem might read on.--Kmhkmh (talk) 23:25, 8 January 2010 (UTC)

Is the following structure in compliance with the requirements?:

1. Introduction. (Until "When the above statement". Move the last two paragraphs to the "History" chapter.)

2. Popular solution

3. Conditional solution

4. Aids to understanding

5. History (general & chronological)

• Similar problems
  
• Monty Hall
  
• American Statistician
  
• Parade
  

6. Arguments and methods (detailed)

• Conditional or not
  
• Variants
  
• Bayesian analysis
  

7. Links and references
Heptalogos (talk) 11:47, 9 January 2010 (UTC)

That looks like feasible approach to me, alternatively i'd like to suggest te following structure maybe slightly better suited for a compromise:

1. Introduction (as is)

2.Problem (as is)

3.Solution (unconditional as is)

4.Aids to understanding (as is)

4.1 Why the probability is not 1/2

4.2 Increasing the number of doors

4.3 Chance of Picking Goat With the Assumption of Switching

4.4 Simulation

5.Detailed Mathematical analysis (contains all "advanced"/more complicated mathematical treatments)

5.1 conditional solution (basically the old "Probabilistic solution - 1991" as is)

5.2 Variants - Slightly Modified Problems (as is)

5.2.1 Other host behaviors

5.2.2 N doors

5.2.3 Quantum version

5.3 Bayesian analysis

5.x other math aspects

6. Psychological analysis (here Krauss & Wang, Mueser,Granberg and others could be treated in greater detail)

7. Sources of confusion (can treat math and psychological aspects together or alternatively moved in subchapters of 5 and 6

8. History of the Problem (as is)

9. See also

10. References

11. External links

From my perspective either suggestion might be a starting point for the mediation.--Kmhkmh (talk) 13:01, 9 January 2010 (UTC)

featured status

Given the recent changes in particular, but also the constant quarrel and maybe latent edit warring. I think it is time to review the featured status. This doesn't have to done right now and might be combined with the mediation procedure (or afterwards) but it should be done. Because the current or future article might be somewhat to significantly different from what was reviewed in 2005. Aside from some of problems listed further of the current article stability is also a criteria for a featured article.--Kmhkmh (talk) 01:47, 8 January 2010 (UTC)

I agree to literally all you say. But an accurate/representative summary of how the problem was treated in reputable literature cannot at all be created without a (our) perception of it. So some of your points are literally useless. Let's do it your way, fully objective, consequently, and replace the article by a list of all reliable sources. Not even a choice of quotes of course. You think that's the essence of the featured status? Heptalogos (talk) 12:01, 8 January 2010 (UTC)

Or could it be that you are suffering from the bad symptoms of our inspiration? The same inspiration that created the featured article, while the bad symptoms are almost all in the talk pages. I like your 'not good' stuff, but the 'discussion' paragraph is largely pointless for the article. Heptalogos (talk) 12:11, 8 January 2010 (UTC)

The spirit that created the originally featured article has nothing to do with the endless and ultimately rather boring discussion that followed the 5 years after (in particular the last year, when I paid some attention to it). People are still arguing about changing the article in a way that essentially makes vos Savant or Morgan look "more right", it is just done in more subtle ways. As in "who is mentioned first", "Who is not solving the real MHP", "who should be considered a variant", "what should be moved to separate article", "should both approaches be described in a combined fashion" or for the latest the odd section titles described above. Quite often in the discussion people seem to willfully ignoring or misrepresenting sources not fitting their POV as well as the statements of other participants. If you look at the edit history of some of the involved participants, it also makes you wonder.... Imho the whole thing is as petty and pointless as the original squabble between vos Savant and Morgan, in fact this seems to the wikipedia extension of it.

If you summarize the reputable literature, it is rather obvious that the article needs to contain both, an unconditional and a conditional treatment. Yet here we are, having a year long struggle of how to implement/realize the obvious and having "proxy battles" about marginal differences (section titles, who goes first, etc.). And for intermission we also doubt the obvious by inserting our own WP:OR and giving our own personal version of the real MHP and judge which reputable literature is wrong and which is right according to it. This is Wikipedia at its worst as far as constructive collaboration is concerned. It might be different though if you are here for the show or for sociological research or other reasons.--Kmhkmh (talk) 13:14, 8 January 2010 (UTC)

I agree to most of what you say, but the irony is that everything you write after the 'good' and 'not good' is about the same kind of drama. Try to look at it this way: the article really has improved over the last year. Apart from that, people are learning on the talk pages. At least recreating. Do you maybe know where suggestions can be assigned for a background discussion forum? Heptalogos (talk) 14:39, 8 January 2010 (UTC)

My point is that the article has not significantly (or at all) improved over the last 6 (or even 12) months. The only positive outcome the quarrel has produced are some additional sources, which is arguably good but not that important since the article due to wealth publication tends to rather oversourced than undersourced anyhow. Neglecting some the latest changes it has barely managed not to get worse (probably mostly due due to Rick Block constantly editing out the biggest nonsense). I would agree however that it still has significantly improved over the 2005/2006 version that became a featured article (see [9]). Looking at the early version however I wonder why it got featured at all, presumably the criteria and selection were still somewhat less strict back then. I understand that people learn on discussion pages and that a learning phase might be required in some discussions. However the main or strictly speaking sole purpose of this page is just (constructive) collaboration discussion to improve the article (which i barely see for last 9 months now, though the formal mediation might be bring some difference here). If people just want to discuss/argue their views of the problem, they can do that here Talk:Monty_Hall_problem/Arguments (see template at the top of the page as well), at another internal page created for such a purpose or outside Wikipedia (web fori, usenet, irc, real life), but ideally not on this discussion page. Anyhow just my observation or 2 cents if you will. I do not intend to join the neverending debate for long, aside from maybe helping in the mediation as this would be a more promising constructive attempt.--Kmhkmh (talk) 15:52, 8 January 2010 (UTC)

Wikipedia is intended to work on a consensus basis, recognizing reliable published sources. You have chosen to not be part of the consensus. And the will of the consensus continues to be rebuffed.

I may be the only active editor who came here simply as a reader of the article. In October, 2008, it was horrible. It is orders of magnitude more useful now. And could still be a lot better. FA or not. Glkanter (talk) 15:28, 8 January 2010 (UTC)

I agree with Glkanter. You have chosen not to take part in most of the discussion yet you presume to tell us how the article should be edited. There is strong feeling amongst many editors that the article does not explain the basic puzzle and solution very well. This is a major failing in an encyclopedia for the general public that needs be be addressed.

You refer to 'latent edit warring'. This is how WP is meant to work. Editors should discuss issues to reach a consensus then edit the article appropriately. The fact that you have intentionally absented yourself from this process does not give you any special rights here. Martin Hogbin (talk) 15:57, 8 January 2010 (UTC)

• I'm neither telling anybody how the article should be edited nor I'm claiming any "special rights", but I was outlining what follows directly from the wikipedia guidelines (and common sense actually). There is no problem with editors wanting to have a simple explanation. In fact we have one prominently featured early in the article (though under a questionable section header). There is however a problem with editors wanting to edit out everything other than "their" simple unconditional solution and who in doubt even do not mind to resort to unsourced material and apparently want the article to create the impression that the simple unconditional solution is all that there is to MHP.
• The fact that Wikipedia for the most part primarily targets the general public, does not mean we write a Wikipedia for Dummies and it does not mean WP only contains material "that everybody can understand". WP collects the knowledge of the world and that means a comprehensive treatment of topics. The important thing here is that articles are properly structured, i.e. information/content requiring a different level of background knowledge is in different chapters, with more complicated treatments and extensions towards the end of the article (which we kinda have here as well).
• 'latent edit warring' is not how WP is supposed to work. It is supposed to work by constructive collaboration not by never ending quarrels over essentially the same things and editing things back and forth. It is supposed to work by achieving a reasonable compromise/result which adheres to WP guidelines and then edit the article in agreement. Maybe the mediation will achieve that, we'll see.
• And finally regarding Glkanter's point. Wikipedia is not just some arbitrary consensus by currently active editors somehow using some reliable sources. Wikipedia is a consensus within the WP guidelines and representing the (available) sources appropriately. Or to put it this way there is no such thing in WP as consensus outside the guidelines or that misrepresent sources.

This is only partly true. It may be that 90% of WP is actually arbitrary consensus, while 90% of the editors sees no issues in it and leaves it unquestioned. As long as people agree with it, most people won't bother to request resources. Check this site: Conditional probability. Where do all text and examples come from? What about the definition of the main subject in de second line: "the possible outcomes of the experiment are reduced to B". It's simply an editor's opinion, but most editors simply agree with it. That's WP also. Heptalogos (talk) 21:20, 8 January 2010 (UTC)

• I do however agree that if the current problems are fixed this version can be seen as an improvement over October 2008 and having the unconditional and the conditional solution clearly separated is a plus ("different background knowledge in different chapters"). However this does not mean the criticism of the unconditional can simply be ignored, but it can be discussed in a separate section comparing both approaches or in the section of the conditional solution.

Anyhow I'm off until the mediation assuming we get one anytime soon)--Kmhkmh (talk) 17:20, 8 January 2010 (UTC)

Ugh! More Straw Men. Enough!

We call them Aunt Sallies in the UK. Knhkmh has made up a list of mad things he claims we all want to do just to show how bad we are. Martin Hogbin (talk) 10:44, 9 January 2010 (UTC)

Where does this presumption that the 'consensus' editors respect Wikipedia guidelines less than you, and Rick, and Nijdam (oh, please) come from? I presume everybody is operating in good faith, until they demonstrate, usually via some hipocracy, otherwise. Your interpretation of Wikipedia's guidelines has merit, just like anyone else's. To present it as a fact that some violation has or will occur is hardly appropriate or supported by the writings of any editor, including Glkanter. And it ignores the prevailing Morgan POV of the current article. Glkanter (talk) 17:40, 8 January 2010 (UTC)

What EXACTLY was the original Parade problem statement?

It seems there is some variations in what the actual problem said. RussAbbott had recently changed the wording of the problem in a minor way, apparently to make it read better to him. Since it is supposed to be a quote, I went off to the "external link" for MvS's web site, as listed at the bottom of the article, and cut-and-pasted what she lists as the original question. Here that is, verbatim:

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

I did post that change with it a snide comment, referring to how Morgan had significantly changed the meaning of the problem by rewording it. I guess Rick took offense, and "changed" it back to what he says appears in a "copy of the column as it was published." That consisted of some insiginicant changes: two in puncuation (the first period becomes a colon, and the first comma in the second sentence becoems a semicolon), and using "No." instead of "#" to mean "number." But two minor wording changes were also included, inserting the words "then" in "He then says to you," and removing "of doors" from the end.

The problem is, I don't have a copy of the column (it would be helpful to post it, Rick) but I have seen numerous variations in the alleged "quotations" of this problem in literature. And what I consider to be the best source amid conflicting ones, MvS quoting herself, agrees with my version:

1. MvS's book The Power of Logical Thinking is exactly as I listed it, except it uses "number" instead of "#". I consider that to be just a change in editorial style, maybe even done without her knowledge.
2. Rosenhaus quotes that exactly; but does attribute it to the book, and not the column.
3. Grinstead and Snell substitute "Monty Hall's Let's make a Deal!" for "a game show," and "Monty" for "he" later on. They also move "You're given a choice of three doors" to the second sentence, separating it from what I listed with a comma. And they don't use any form of "#", just listing the bare number.
4. Krauss and Wang use a semicolon where Rick did, and capitalized "Number" wherever it appears in place of "#". But they also added Rick's "then" and changed "pick door #2" to "switch to Door Number 2".
5. Morgan takes significant liberties with the quote, which are discussed elsewhere. They include using "No." and Rick's "then."
6. Are there any others?

My question is, is there an internet source to verify the actual (not quoted) version? And if not, shouldn't we trust MvS's own quote of herself over all others, since there seems to be a inexplicible tendency to misquote it? JeffJor (talk) 17:54, 8 January 2010 (UTC)

Oh for Christ's sake, you think I'm LYING? I have a printout from a microfilm reader of the Sept 9, 1990 edition of Parade Magazine (as published with the Knoxville News Sentinel). The quote as it has been in the article for quite a long time is exact (including punctuation and capitalization). I am NOT going to scan the copy I have and post it. If you don't believe me, you can verify this for yourself (go find a library that has a microfilm copy of a newspaper that included the supplements). -- Rick Block (talk) 03:00, 9 January 2010 (UTC)

No, I don't think you are lying, Rick. I said no such thing, and had no intent to imnply it. But I had actually cut-and-pasted my version from a direct source, so I felt about the same way you do about the edit you made. And I didn't go on to accuse you of calling me a liar. The fact that I didn't put it back to what that source says, and asked for verification and discussion, shows that I am exhibiting a great deal more integrity than you are blaming me for.

And, I do think (1) That microfilm of a newspaper can be mis-read when it comes to the difference between a comma and a semi-colon; (2) That sometimes we see what we want to see even if it isn't there, and (3) that it just might be possible that some editors - like, say, those in Knoxville - "corrected" what they thought was incorrect usage. We actually have evidence of these sorts of thing, since Morgan grossly misquoted it and the internet reference and the on-line version of MvS' book contain at least one such change. Again, I'm not accusing you of any of these things, I'm saying we can't know unless we can all see your source.

The point is, I don't know what was originally published; but we have an easily-verifiable source that anybody can see, and that doesn't require looking at microfilm and/or wondering if some phantom editor changed something. And since you were the one who took it upon yourself to make those insignificant changes (unless you think there is a significance?), yes I do think the onus is on you to prove it is correct when MvS herself quotes it differently. We can change the reference to her book, which is about the column, if you desire, and remove all these difficulties. Or keep it as is, and reference Parade Magazine, as published in the Knoxville News Sentinel.

And this digression kinda echos the entire problem with this article. It seems there are multiple versions of "truth," and the discussion tends to be more centered on "Why can't all you idiots see the truth the way I do?" rather than handling the different "truths" for what they are - truths that are based on different sets of assumptions. Morgan, et al, did solve an actual ptoblem; but it clearly (sources, including MvS, say so, Rick; and the only significant difference in their interpretation is whether door numbers are important, unless you know of anoither. Everything else they criticze is what they say MvS assumed, which is not a difference in interpretation) isn't the one Marilyn intended, or what her problem (which she formatted, not Craig Whitaker) sematically says. JeffJor (talk) 17:15, 11 January 2010 (UTC)

I agree that it is important that we get this right. Just out of interest, does anyone know if Craig Whitaker was a real person? If so has he ever made any comment about the subject? Martin Hogbin (talk) 18:22, 8 January 2010 (UTC)

Per above, if you think it's not right feel free to verify it yourself. Craig Whitaker is (well, at least was) a real person. My understanding from a reliable source (that I will not divulge, which means it's not a "fact" as far as Wikipedia is concerned) is that some reporter (surprisingly, not John Tierney from the NY Times) tracked him down and that what appeared in Parade is not exactly what he wrote (if that's where you're going) but omitted that he thought the answer could be 1/2 or 1/3 depending on what was assumed. -- Rick Block (talk) 03:00, 9 January 2010 (UTC)

Since I, too, live in Columbia Maryland, I looked him up in the phone book. I found no Craigs. And I didn't want to bother the ten-or-so Whitaker families to ask, since it is likely he graduated from one of our High Schools about fifteen years ago. And if we know it isn't exactly what Craig wrote (as per Rick Block's recollection), we need to remove his name from the reference list and make it refer to MvS. Quote her, quoting Craig, and don't imply Craig is an expert at anything. JeffJor (talk) 17:15, 11 January 2010 (UTC)

I was asking just as a matter of interest, I do not doubt any of what you say. I just thought that, if he could be contacted, it would have been interesting to ask him what exactly he had in mind. It did just occur to me that he might have been someone made up by the editor or vS. It is good to know that he is real. I wonder what the makes of the furore that his question created.

Similarly I do not think that Jeff was accusing you or anyone else of anything. Because the exact question is important in statistics, both Jeff and I think that it is necessary to get the original question exactly right. Thank you for confirming this. The matter is of particular importance to some of us because of the way that, in our opinion, Morgan morphed the question into a different one. Martin Hogbin (talk) 10:34, 9 January 2010 (UTC)

What is the best internet source available? Is it the MvS site? Is the Parade edition available in a public library? Do we have arguments about difference between both? If so, what is the WP policy about reliability of non-internet sources? Heptalogos (talk) 14:11, 9 January 2010 (UTC)

Not every citation needs an online source although I agree this is desirable. The article currently cites Whitaker's letter in Parade as this is the definitive source. Martin Hogbin (talk) 15:52, 9 January 2010 (UTC)

The policy regarding sources is Wikipedia:Verifiability with more detailed guidelines at Wikipedia:Reliable sources, and you basically have your question backwards. From Wikipedia:Reliable sources#Quotations: Quotations should be cited to the original source if possible. Parade is a magazine supplement published with hundreds of newspapers (in the U.S.). Microfilm copies of newspapers are available in many public and university libraries. For a long time this quote was indirectly referenced ("as cited by") to an article by Bohl et al. in the 1995 edition of Journal of Recreational Mathematics. As part of the last featured article review I did a large amount of referencing work (one of the concerns was "Huge sections of unsourced content") and as part of this chased down an actual copy of the Sept 9, 1990 edition of Parade (as I mention above).

This entire thread is grossly insulting. I reverted Jeff's change because it was wrong, not because I took offense to his snide comment about Morgan. I really couldn't care less what he thinks about Morgan (or, at this point, pretty much anything else). What I said in my edit summary was "revert to the actual quote - I'm looking at a copy of the column as it was published". In this thread he's both attributing a motivation for my change that he simply made up (which is bad enough) and calling me a liar. Martin echoed Jeff's insult "I agree that it is important that we get this right" (what about "I'm looking at a copy of the column as it was published" is not clear???). And you (Heptalogos) are questioning what the sourcing policy is (as if any internet source could possibly be more reliable than the actual magazine).

I'm trying very hard not to say something grossly insulting in return here. Let's just say that I think all three of you should apologize. -- Rick Block (talk) 16:25, 9 January 2010 (UTC)

+1 I agree that this thread is entirely pointless and somewhat surreal. I'd suggest to simply ignore it.--Kmhkmh (talk) 00:42, 10 January 2010 (UTC)

I can see why Rick has taken exception. His edits, his research, and his very integrity have, in his mind, been attacked, without provocation or fact-based support.

Welcome to my world, Rick! Rather than get an apology, I had 2 guys file an RfC on me for a much more offensive situation than this. Aint Karma a b----, Rick? Glkanter (talk) 16:45, 9 January 2010 (UTC)

Yes, there's an RfC open on your behavior. Your post here is yet another example of your bad behavior. I invite anyone reading this to add their opinions to Wikipedia:Requests for comment/Glkanter. -- Rick Block (talk) 17:28, 9 January 2010 (UTC)

Rick, you are taking this far too personally. I, and I suspect Jeff, just thought that there was some doubt as to the exact wording of the problem, looking at the various sources on the subject. You have confirmed that the current wording is exactly as it is in Parade magazine, some good work on your part. That is the end of the matter as far as I am concerned.

Heptalogos was, I think, just suggesting that some online references would be good (if there are any for the exact quote) so that readers and future editors can verify the problem statement for themselves. Martin Hogbin (talk) 17:48, 9 January 2010 (UTC)

Since the reference is to the printed magazine, it can't be verified definitively against any online source, and so the question of what online source is the best to use to verify the quote is correct is meaningless. At this point, Wikipedia is as good as any other online source - actually, IMO, better since anyone is free to verify it with their own eyes (as I have done) and then correct what it says. In addition, it's a featured article meaning many editors have closely looked at the entire article so the chances that someone has actually verified the quote here is correct are quite high (this applies to any featured article, not just this one).

And, as far as taking it personally, I think I'm taking it in the spirit in which it was intended. -- Rick Block (talk) 18:54, 9 January 2010 (UTC)

Let's stay with the facts and strip them from complex emotions. This is what I understand of it:
1. The Whitaker quote in this article is different from the quote on the MvS site, which is claiming to be an original Parade publishment.
2. A WP-editor, senior Admin, claims to have seen the original Parade article which is exactly the same as in the article.
3. Quotations should be cited to the original source if possible.
4. Any internet source is less reliable than the actual magazine.
5. We have two internet sources quoting the original source: senior Admin and MvS.com.
6. Senior Admin is more explicit in the claim that his quote is very exact.
7. In absence of written policy, do we have any decisional law (jurisdiction) on this? Heptalogos (talk) 20:03, 9 January 2010 (UTC)

It seems to me now, from this source, that Marilyn is about just as explicit in her claim of excellent quoting. An interesting sentence in that, which may even give a hint towards the cause of apparent disparity, is: "Here are both (question and reply), as they first stood". Indeed, MvS site introduction states: "This material in this article was originally published in PARADE magazine in 1990 and 1991". Rick, is the Sept 9, 1990 edition of Parade Magazine, the first one about the problem? Heptalogos (talk) 22:45, 9 January 2010 (UTC)

'...then perhaps we would' and the page stops! What?! We would 'what'?!? I gotta know!

These guys are sorry excuses for whatever it is they are. And we've got the 5th Beatle right here on Wikipedia. Glkanter (talk) 23:05, 9 January 2010 (UTC)

Hard to find the complete PDF, but here's another interesting source: [10]. Heptalogos (talk) 23:45, 9 January 2010 (UTC)

The initial column was Sept 9, 1990. Well, at least, that's what I'm claiming. How about if you verify what the magazine actually says yourself? Just go to a library and look it up. There's a list of newspapers that currently carry it here. Call your local public library and ask if they have microfilm of any of these newspapers (from 1990), including the Sunday supplement sections (specifically Parade Magazine). And, yes, I'm saying in her reply to Morgan et al. vos Savant (like Morgan et al.) trivially misquoted her column. She used a comma rather than semicolon following "Behind one is a car", used "#" rather than "No.", and dropped "then" and added "of doors" in the last sentence.

JSTOR makes only the first page of the references it carries available for free. I have the next page of this one as well. I could tell you what it says, but given how absurd this thread has become I suggest you go to a library (probably a university library for this one) and look it up yourself. -- Rick Block (talk) 01:27, 10 January 2010 (UTC)

On my first visit to the US I might take a look in Parade. In that case I should sign the source witness list, because when I leave here, another editor may ask the same question. I am trying to understand how WP works. But you are convincing and the change seems to be a cosmetic improvement. It makes sense. Marilyn is a proud lady. Heptalogos (talk) 10:18, 10 January 2010 (UTC)

You could try to obtain a reprint of the Parade column as well, see [11]. However, I'm not sure if a reprint obtained this way would necessarily be identical to what was originally published. Another idea would be to find a library (possibly a university library) that might have microfilm of a major US newspaper that carries the magazine. Possible examples would be the Chicago Tribune or the Los Angeles Times. If you're a student or faculty member at a university I'm sure your university library could obtain a copy for you, and if you're not at a university then the reference librarian at any decent public library should be able to help. -- Rick Block (talk) 17:07, 10 January 2010 (UTC)

Rick, I have to take issue with one point you make above. You say, '...vos Savant (like Morgan et al.) trivially misquoted her column...'. I agree that vos Savant's misquotation was trivial but Morgan's was not. It was part of a subtle process that changed the question into something different.

Anyone who has studied the MHP, either here or elsewhere, must know that the exact question is important. Things which at first sight might seem irrelevant turn out to make a critical difference, for example, most people are surprised to be told that it makes a difference whether Monty knows where the car is.

The Morgan misquotation starts to move the problem statement from saying that the host opens a door with and explanation of what that might mean, to the host opens door 3, where it is clearly the intention of the question to specify which door the host opened. These things are important in probability problems and Morgan's misquotation is quite inexcusable. Martin Hogbin (talk) 10:45, 10 January 2010 (UTC)

This is what happens when hosts/producers share information with contestants.

http://www.huffingtonpost.com/2010/01/08/our-little-genius-kiddie-_n_416440.html

To argue that the host indicating to the contestant where the car is located is consistent with the statement "Suppose you're on a game show..." is contradicted by the facts. Glkanter (talk) 18:32, 8 January 2010 (UTC)

Can you be more explicit in what your exact proposal or criticism is about? Heptalogos (talk) 20:54, 8 January 2010 (UTC)

Sure. Morgan, and others call the simple solutions 'false'. Then they claim to 'prove' this by concocting a host bias, that presumably the contestant is aware of.

Issue #1 is that this is not a valid method of dis-proving a solution, this criticizing problem 'B' as a means to discredit problem 'A'.

Issue #2 is that there can be no such transfer of knowledge, in any way, shape or form from the host/producer to the contestant. As this article demonstrates. I've posted 2 Wikipedia articles on this subject previously. Symmetry prevails by definition.

Morgan and others published it. It goes in the article. Thoughtful editors may choose not to over-emphasize Morgan's critique in the article. Glkanter (talk) 21:18, 8 January 2010 (UTC)

OK, can you please move this to the arguments page first? Heptalogos (talk) 21:28, 8 January 2010 (UTC)

I'm done with it. Besides, it's about how to edit the article. That's what this page is for. Glkanter (talk) 21:37, 8 January 2010 (UTC)

How Goes The Formal Mediation Filing?

I tried to sign that I'm willing to go along, or whatever. Is there a place to do this?

Has Nijdam responded? Glkanter (talk) 13:21, 9 January 2010 (UTC)

The request has not been officially filed yet since Nijdam has not responded. I've tried to contact him via email. He hasn't made any edits since Jan 2. I suspect he may be on holiday. I'd like to give him another week or so to respond, but if you're unwilling to wait that long you can certainly file the mediation request yourself (you'd have to rearrange the draft I created a bit). -- Rick Block (talk) 18:07, 9 January 2010 (UTC)

If I filed it without listing Nijdam, is it still valid? Would Nijdam or any other editor be able to claim I had filed a 'biased' request? Glkanter (talk) 18:14, 9 January 2010 (UTC)

I think you are maybe misunderstanding the idea of mediation. The mediator will not try and force an agreement on us, they will just try to help us to work together. So, if Nijdam is happy with the mediation process, it will continue. If anybody says that will have nothing to do with it but they will continue to push for their wishes then it cannot work. I do not have much faith in the process now, after failing to get even one side of the argument to agree, but I am happy to give it a go. Martin Hogbin (talk) 18:30, 9 January 2010 (UTC)

So, it's intractable, then. What official Wikipedia steps remain available to us? Or do we just keep arguing and over-editing each other in the article in a non-3RR manner? Glkanter (talk) 18:39, 9 January 2010 (UTC)

I have done some editing

Having tried in vain to reach any form of consensus I have made a few edits to see what the general reaction is.

I have deleted the unsourced comment about door numbers and replaced it with a comment (citing Seymann) that Morgan address their interpretation of the problem, in that specific doors are identified in the problem statement.

I have added what should be an uncontroversial explanation of the existing diagram. Martin Hogbin (talk) 14:35, 9 January 2010 (UTC)

Kmhkmh's criticism about the unsourced comment is in the 'Recent changes' chapter on this page. I added the source and explanation to that, so I guess we'd better check or discuss it before deleting the entire thing. Heptalogos (talk) 18:44, 9 January 2010 (UTC)

The point is that the section I removed seemed to be a view that is pretty well unique to you, and certainly not one I have seen mentioned in any reliable source. I think the fact that the numbers of the doors may not be intended to be important is better covered by Seymann's comment on the Morgan paper, even though he does not specifically state this.

I think that you are making much the same point but in a different way. Martin Hogbin (talk) 18:53, 9 January 2010 (UTC)

"Unique to you": do you know that Rick added this view? Heptalogos (talk) 20:10, 9 January 2010 (UTC)

Sorry, I though it was you who was promoting this possibility. Martin Hogbin (talk) 21:18, 9 January 2010 (UTC)

What view did I add? -- Rick Block (talk) 01:29, 10 January 2010 (UTC)

I checked the history and thought I saw that you were the one adding the paragraph in the Problem section about 'fixed door numbers'. Isn't that true? Heptalogos (talk) 22:18, 10 January 2010 (UTC)

I found another source. Please check under 'Recent changes'. I may understand your question about Whitaker being a real (third) person. Heptalogos (talk) 22:57, 9 January 2010 (UTC)

With the above changes I am not that unhappy with the article. I would still like to.

1) Rename 'Popular solution - 1975' maybe 'Simple solution' are just 'Popular solution' again.

The year really has no meaning here.

2) Rename 'Probabilistic solution' 'Conditional solution'.

All solutions are probabilistic, this is the conditional solution.

3) Move the 'Aids to understanding' section to be immediately after 'Popular solution'.

If you read this section you will see that none of it relates to the conditional problem/solution

Martin Hogbin (talk) 16:05, 9 January 2010 (UTC)

I've gone ahead and deleted the dates from the headings. It seems clear there's no support for including these dates. -- Rick Block (talk) 16:39, 9 January 2010 (UTC)

How about we do away with the 'History' section, and present the Solution sources chronologically? With headings and sub-headings for clarity? Then, dates would be very useful. Glkanter (talk) 17:25, 9 January 2010 (UTC)

Thanks. Do you see my point about the 'Aids to understanding' section? This is aimed at the general reader, who may not accept or understand the solutions presented. Later sections are for more advanced readers. Martin Hogbin (talk) 17:35, 9 January 2010 (UTC)

I still think we only need one Solution section including both an unconditional style and conditional style of solution. In my opinion, the more you separate the "popular solution" and the "conditional solution" the less NPOV you make it. Please think carefully about your reason for wanting to avoid a conditional solution up front. Is it really because it's a more complicated approach, or is it because it doesn't fit your POV that the problem should be approached unconditionally? -- Rick Block (talk) 17:51, 9 January 2010 (UTC)

My main reason for wanting to change this article has always been that it fails to provide a simple and convincing solution and explanation for the general reader. I think you have lost sight of just how hard it is for most people to understand and accept the simple solution to the non-conditional problem. The last sentence in the lead says, 'Even when given a completely unambiguous statement of the Monty Hall problem, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief'. If we just state the facts without making them understood by our readers, no matter how well they are supported by reliable sources, we fail in our job of producing a good encyclopedia. The main point of the MHP is that you can tell people the answer, and still they do not believe you.

My POV is that the issue of conditionality is not that important at the start of the article, although it should be discussed later as it was raised in a published source. That is why I say that I want to treat the problem non-conditionally (meaning just not dealing with that particular issue) rather than unconditionally, to start with. I am happy to continue to discuss the subject of conditional probability on the arguments page with anyone who is interested. Martin Hogbin (talk) 18:22, 9 January 2010 (UTC)

I've mentioned this before (perhaps I should look for a published source supporting this view), but IMO at least one reason many people disbelieve the typical unconditional answer is because it does not have the same form as how people generally interpret the problem - in particular, the fact that the host has opened a particular door completely vanishes. Most people (the K&W study does support this) internalize the question as asking what is the probability in a specific case, e.g. given the player picks door 1 and the host opens door 3. The unconditional solution isn't restricted to this case. I think a solution that addresses BOTH the unconditional situation and the conditional situation is likely to be far more convincing than only an unconditional solution. -- Rick Block (talk) 19:50, 9 January 2010 (UTC)

This really is OR. K&W showed that door numbers generally confused people and that people generally did better when they were not involved. My take on this is that the problem is more easily explained and understood without door numbers. Just as we do now to start with.

I am sure that nobody finds the problem hard just because they think it might matter which door the host opens. Most people miss this point completely, and assume that it cannot possibly make any difference (whereas in truth it could possibly make a difference but does not actually do so, with consistent assumptions). I certainly did not imagine that the door opened by the host could matter, and it is not even mentioned in the 'Three prisoners problem'. More to the point there is no source that I am aware of that claims that this possibility is what makes the problem difficult. Martin Hogbin (talk) 20:14, 9 January 2010 (UTC)

Though I kinda agree with you here, I do on the other hand not mind having 2 different solution sections (unconditional/simple and conditional/detailed mathematical analysis) - in particular if this provides compromise everybody might be live with. If one takes a step back from what he might consider the "optimal" version of article from his perspective but rather thinks of an acceptable or sufficient version (not being optimal to oneself but acceptable to all involved editors and readers in general), then this should be the way to go imho.

Also separating "easy" from the "hard" is definitely good idea. This is a general organizing principle for a well written article/book/whatever anyhow. The fact that this approach might be convenient for Martin potential POV ("it has to be solved unconditional") is irrelevant, since the advantage of that approach are real and having nothing to with Martin. The German probability book, I've mentioned occasionally (Henze) for instance pursues exactly that approach. It mentions MHP in the introduction as an example for probability theory or problems in the public domain and then later gives the unconditional solution. Much later after having laid some theoretical groundwork and having introduced conditional probabilities he revisits the problem for a more detailed analysis and a conditional solution. I see no reason why the our article can't do the same.--Kmhkmh (talk) 20:42, 9 January 2010 (UTC)

Maybe we are moving towards some kind of acceptable compromise here. I wonder what others think? Martin Hogbin (talk) 21:15, 9 January 2010 (UTC)

I agree to most suggestions, especially to the terms 'Simple solution' and 'Conditional solution'. We must remember that the 'Monty Hall problem' is basically a paradox simply solved by the popular solution, and that only specific problem statements, like in Parade, or specific interpretations of them, need conditional solution. This is another argument for starting with the simple solution. Also indeed, 'Sources of confusion' should really be (far) below 'Aids to understanding'. But I am getting into trouble as to where chapters should be, and how they should be structured. It tends to become rather POV or endlessly arguable if we don't use any objective structure. As Glkanter proposes: use chronology. I think it may be good if the whole article is made up that way, which will naturally present the entire scope as it grows in complexity and perspectives. I do understand that most 'normal' subjects are better off with a simple definition and explanation first, but if there's one thing this issue has proven, it is the fact that there is no single truth here. There's lots of different questions with lots of different answers and lots of different methods. The introduction may spend some words on it, to explain the choice for chronology. This should really reduce our disagreements! What is important in this scenario, is to have an exhausting 'contents' tree, from which one can easily jump to the section of choice. The contents section should give enough description to have a fair idea of what it's about. Heptalogos (talk) 22:01, 9 January 2010 (UTC)

Chronological, but none of those 'pointy, POV dates' will be allowed. Glkanter (talk) 22:15, 9 January 2010 (UTC)

Chronology contradicts my suggestion and what Martin seems to be indicating as well. So you cannot support the above (organizing by content and difficulty level) and wanting a chronological organization for the sections, it is either or here. Again I'm getting the impression we are moving 1 step ahead and 2 back. As soon as there seems to be some reasonable common ground, another issue is raised or something rather inconsistent statement is put forward as well. --Kmhkmh (talk) 23:03, 9 January 2010 (UTC)

As a matter of fact I can support changes to the current structure as well as favoring another structure. It's an expression of flexibility which enables reinforcement of common ground, while at the same time offers an opportunity to improve significantly in the long term. Although I am very aware of the extra energy it takes for the time being. If we all keep getting tired, I think we indeed keep getting tired, for a much longer time. Heptalogos (talk) 23:21, 9 January 2010 (UTC)

Why Didn't Whitaker Write To Morgan, et al, Instead?

Because they don't have a general interest column read by millions every week published as a supplement to hundreds of newspapers across America.

In her letter to The American Statistician vos Savant directly tells Morgan her interpretation. She tells them *her* interpretation of Whitaker's letter. But these guys claim to know these things better than vos Savant herself. She had helped to educate over 1,000 PhDs on this paradox, she says. But not this Professor Morgan and his 3 assistants. They are different. Or, having spent 15 months on this article, maybe not so different.

And if Whitaker is fictional? Then vos Savant and her publisher made him up. And they know what they meant to ask.

So, back to the article. How will the article cover the aspect of Morgan calling all simple solutions 'false'? That means Selvin, vos Savant, Adams, Devlin, etc., etc. all are wrong. Sad state of affairs in academia these day. Hasn't been the same since 1991, really. All because Morgan claims a game show host can tell a contestant where the car is.

Will it lead off the solution section? Go last, but bold? Mentioned after each of the other solutions? I want to know. Where else will this revelation be placed in the article? How many times? Because Selvin already did the conditional solution, in 1975. What is it that Morgan's paper is noteworthy for then? The only thing left is calling the simple solutions 'false'. I guess countless Professors, etc. haven't gotten the word on this paper, yet, because they still teach it.

Morgan says this: "...(the producer)...is free to consider a variety of factors in determining how the game will be run." That's correct. Including all applicable laws. Game show hosts and producers do not tell contestants where the car is. Glkanter (talk) 13:55, 10 January 2010 (UTC)

What is YOUR suggestion? -- Rick Block (talk) 14:50, 10 January 2010 (UTC)

What I understand, and why, I have made abundantly clear. I have, and will continue to share my views with the consensus of editors.

But, you're the long-standing defender of Morgan's paper. What do you think are the new issues the paper brought forth in 1991? Why is it significant? Glkanter (talk) 15:39, 10 January 2010 (UTC)

I have just added a section [12] to my Morgan criticism page, which shows the question that Morgan have actually answered. I would be very interested to hear from both of you whether you agree that Morgan's paper actually addresses the question that I have stated. This may stop some pointless argument. Please leave your comments on the associated talk page. The footnotes are simply to address Morgans claim to have given a solution based only on information given in the problem statement. For the moment, do you both agree that the Morgan paper is a fair answer to my stated question? Martin Hogbin (talk) 15:08, 10 January 2010 (UTC)

I agree that your problem statement is one wording of what Morgan et al. calls the "vos Savant" scenario. You might note that Gillman addresses this same problem as well. -- Rick Block (talk) 16:30, 10 January 2010 (UTC)

It looks as if we can agree on the exact question that Morgan actually answer. Martin Hogbin (talk) 17:09, 10 January 2010 (UTC)

You are being rather kind to Morgan though. The fail to mention in their paper that: the car is originally randomly placed, the player chooses randomly, the host can never open the player's originally chosen door, and the host must always offer the swap. Perhaps they take these rules to be somehow transcluded from vos Savant's analysis or elsewhere. Martin Hogbin (talk) 17:43, 10 January 2010 (UTC)

Falk, also. It's one of the versions Krauss and Wang address, too. -- Rick Block (talk) 16:34, 10 January 2010 (UTC)

Glkanter, do you agree that Morgan answer my stated question correctly? Martin Hogbin (talk) 17:11, 10 January 2010 (UTC)

You can find the question that they answered here [13]. Note that I do not claim that this is the MHP. In fact I assert that it is not. Martin Hogbin (talk) 23:53, 10 January 2010 (UTC)

This New Archiving Taking Place

I just took a look at archive #12. I think sections are being moved, but not in the order they were created. So the archive does not preserve the original discussions as they took place.

Would anyone mind confirming this? Is this the way archiving should work? Glkanter (talk) 13:05, 11 January 2010 (UTC)

I've asked the bot owner. See user talk:Misza13#Archive order. -- Rick Block (talk) 19:48, 11 January 2010 (UTC)

Thanks for doing that, Rick. I just read his response. He says that's the way it's supposed to work. I'm only experienced in 'data' archiving, not 'conversation' archiving. I really don't know, but it seems like it defeats the purpose. It never occurred to me that MHP archives 1 - 11 were built that way. Glkanter (talk) 00:39, 12 January 2010 (UTC)

So, What Are The Significant Events, And Why, Of The Monty Hall Problem Paradox

Some people certainly didn't like the chronology I posted on the this talk page. Heck, it was vandalized, then they put up an RfC/U on me because of it.

And when I added the year to the Solution sections, an edit war damn near broke out. And editors turned on editors.

So, who, what, where, when, and why? But especially this Morgan paper. It seems its only contribution is to use an unimaginably wide paint brush to call the unconditional solutions false. Glkanter (talk) 13:32, 11 January 2010 (UTC)

Glkanter, if you would answer whether you think Morgan have answered this question correctly, it might throw some light on the subject. Martin Hogbin (talk) 13:47, 11 January 2010 (UTC)

I looked at it earlier this morning. First, I would need to know why it even matters. Otherwise, I just can't bend my brain to comprehend that stuff. 6 footnotes? Sorry, it's just not an area I'm strong in, or that I have much interest in. Nor do I think my opinion on that OR is relevant to editing the article Glkanter (talk) 13:59, 11 January 2010 (UTC)

Ignore the footnotes for the moment, just read the question. I am trying to reach some kind of resolution over your, often repeated point, 'Suppose you're on a game show'. Note that my question does not suggest that perspective, it simply asks you to solve a problem based only on the information given in the problem statement. Do you agree that Morgan have answered that question correctly? Martin Hogbin (talk) 14:19, 11 January 2010 (UTC)

What's the point? Who are you trying to influence? And why? Just look at Nijdam's newest contribution to the discussion. But they won't give a straight answer to 'Is The Contestant Aware?' or 'How Can Huckleberry Do Better By Knowing The Equal Goat Door Constraint?'. I prefer to expose intellectual dishonesty, rather than enable it. Glkanter (talk) 17:12, 11 January 2010 (UTC)

See Monty Hall problem#History of the problem. Morgan et al. is one of the "Over 40 papers have been published about this problem in academic journals and the popular press". Although the history section doesn't say this, it is (to my knowledge) the first paper specifically addressing the problem published in an academic peer reviewed statistics journal. -- Rick Block (talk) 19:55, 11 January 2010 (UTC)

I guess it's also the only published paper on the issue that vos Savant publicly replied to. Heptalogos (talk) 20:47, 11 January 2010 (UTC)

How do both of your answers correspond to either advancing MHP Paradox knowledge, or following Wikipedia principals? I don't see them doing much of either. Glkanter (talk) 21:20, 11 January 2010 (UTC)

I'm quite sure that my obvious answer to you will be of no benefit, so I'll leave it here. Heptalogos (talk) 22:05, 11 January 2010 (UTC)

Not if you don't post it. I have no idea whatsoever you might reply. Glkanter (talk) 22:49, 11 January 2010 (UTC)

Yes, I was anticipating your response, Rick. But you chose not to answer this back then. So, tell me now, how and why is Morgan the Uber-Monty-Hall-Problem-Wikipedia-article-source? Glkanter (talk) 21:31, 11 January 2010 (UTC)

Glkanter, I hate the Morgan paper as much as you do, but unfortunately we are stuck with it to some degree, for the reasons given above. The important thing to me is to see it for what it is, a solution to a somewhat contrived and restrictive formulation of the problem that does not represent the MHP as most people understand it. Martin Hogbin (talk) 23:01, 11 January 2010 (UTC)

Of course. It's published. I said that just yesterday. It has no new point to make (except 'as we contrive it, all unconditional solutions are false'), and with all the article's flaws there's no rationale for it being the focus of, and the 800 lb gorilla looming over every aspect of the article. Martin, we're unnecessarily just arguing with ourselves. By now you know that I understand that Morgan is published, and that gives Rick the ability to cling to it. We're being stifled from our legitimate ability to edit the article as the editorial consensus. What's left to say on the various talk pages, by either 'side'? Nobody is budging, clearly, and the article remains confusing and cluttered to the Wikipedia readers. Glkanter (talk) 23:18, 11 January 2010 (UTC)

(outindent) How is this paper "the focus of, and the 800 lb gorilla looming over every aspect of the article"? I said before (toward the end of #What If Morgan Had Used A Different Variant?) "As far as I can tell the only mention of this POV is in the "Probabilistic solution" section, the 4th paragraph in "Sources of confusion" and a paragraph in "Variants"." and you said "It's in every word except the intro and the Simple solution section." Perhaps we should go through the article paragraph by paragraph starting with "Sources of confusion". Here's a list (based on this version - current as I'm typing).

Sources of confusion, paragraph 1: no Morgan et al.

Sources of confusion, paragraph 2: no Morgan et al.

Sources of confusion, paragraph 3: no Morgan et al.

Sources of confusion, paragraph 4: a mention of Morgan et al.

Why the probability is not 1/2: no Morgan et al.

Increasing the number of doors, paragraph 1: no Morgan et al.

Increasing the number of doors, paragraph 2: no Morgan et al.

Increasing the number of doors, paragraph 3: no Morgan et al.

Chance of picking goat with the assumption of switching: no Morgan et al.

Simulation, paragraph 1: no Morgan et al.

Simulation, paragraph 2: no Morgan et al.

Simulation, paragraph 3: no Morgan et al.

Simulation, paragraph 4: no Morgan et al.

Simulation, paragraph 5: no Morgan et al.

Other host behaviors, paragraph 1:no Morgan et al.

Other host behaviors, paragraph 2:no Morgan et al.

Other host behaviors, paragraph 3:a mention of Morgan et al.

Other host behaviors, table:one of nine cases mentions Morgan et al.

N doors, paragraph 1: no Morgan et al.

N doors, paragraph 2: no Morgan et al.

Quantum version: no Morgan et al.

History of the problem, paragraph 1: no Morgan et al.

History of the problem, paragraph 2: no Morgan et al.

History of the problem, paragraph 3: no Morgan et al.

History of the problem, paragraph 4: no Morgan et al.

History of the problem, paragraph 5: no Morgan et al.

History of the problem, paragraph 6: no Morgan et al.

History of the problem, paragraph 7: no Morgan et al.

History of the problem, paragraph 8: no Morgan et al.

History of the problem, paragraph 9: no Morgan et al.

Bayesian analysis, paragraph 1: no Morgan et al.

Bayesian analysis, paragraph 2: no Morgan et al.

Bayesian analysis, paragraph 3: no Morgan et al.

Bayesian analysis, paragraph 4: no Morgan et al.

Bayesian analysis, paragraph 5: no Morgan et al.

Bayesian analysis, paragraph 6: no Morgan et al.

Bayesian analysis, paragraph 7: no Morgan et al.

Bayesian analysis, paragraph 8: no Morgan et al.

Bayesian analysis, paragraph 9: no Morgan et al.

Bayesian analysis, paragraph 10: no Morgan et al.

Bayesian analysis, paragraph 11: no Morgan et al.

Bayesian analysis, paragraph 12: no Morgan et al.

Let's count, shall we? I come up with 42 paragraphs (starting with "Sources of confusion") and 3 references to Morgan et al. Does this make it "the focus of, and the 800 lb gorilla looming over every aspect of the article" and "It's in every word except the intro and the Simple solution section"? If you're not suggesting eliminating Morgan et al. completely from the article (which you keep claiming is NOT what you're suggesting), then what are you suggesting? -- Rick Block (talk) 15:03, 12 January 2010 (UTC)

Last February I wrote that 5% of the article added value, the other 95% was waste. I understand Wikipedia's policy's better now, so I'm willing to double it. Make it 10%.

The very existence (and certainly the content) of Aids and Sources shows a pre-disposition to Morgan's claim that the simple solutions are all false and/or inadequate. The existence of all the variants, except the Forgetful (Random) Monty sprout from Morgan. Morgan gave license to these other contrivances you call variants that are more appropriate for a shell game than a game show. Only the forgetful Monty informs the contestant at the same time as the observer, by revealing the car. All the others rely on collusion or ESP.

So Selvin came up with simple and conditional in 1975. vos Savant came up with random (essentially Deal or No Deal) in 1990. Morgan contrives his stuff to claim the simple solutions are false in 1991. Bayesian? I have no comment. History? Shows that a poor job was done earlier in the article. Just call everything after the Solutions sections 'Diversions'. Glkanter (talk) 16:19, 12 January 2010 (UTC)

So, you're suggesting deleting the entire article following the Solution section? Is this the change you think there's a consensus for that you keep complaining you're being prevented from making? -- Rick Block (talk) 19:31, 12 January 2010 (UTC)

Nope. Not at all. The consensus of the editors agreed on the various benefits of the 3 proposals. I'll be one voice of that consensus that makes changes, eventually. Even Dicklyon made note in his comments of Wikipedia violations of UNDUE in the article.

So, why is Morgan significant? The paper strikes me like Paris Hilton. She's celebrated for being a celebrity. Morgan's paper is, in your estimation, anyways, important for where it was published. Not many of us share that POV. I don't believe Wikipedia's policies support that either. Glkanter (talk) 21:32, 12 January 2010 (UTC)

You apparently have a fundamental misunderstanding of Wikipedia:Consensus. Consensus applies to edits, not editors. It is definitely NOT the case that the article will be "open for editing" ONLY to some set of "consensus" editors. If this is what you're looking for you will never get it, by any process at Wikipedia. I keep asking you about specific changes, because that is the ONLY thing consensus applies to. This will perhaps become more clear to you if/when we get to formal mediation. -- Rick Block (talk) 15:32, 13 January 2010 (UTC)

Another Straw Man, aka Aunt Sallie. Don't you have anything better to do with your time? Glkanter (talk) 16:08, 13 January 2010 (UTC)

I'm just trying to understand what you're talking about. You say the article is rife with a pro-Morgan POV and at least imply you think everything after Solutions might as well be deleted. I asked if this is indeed what you are suggesting. Your reply says you're not talking about deleting everything but that you'll be part of a consensus that makes changes, making it sound like some "consensus of editors" will have carte blanche to make whatever changes they collectively want. What I'm saying is that this is not how it works and you're at least implying you know that. OK. So please say what specific changes you are suggesting. Take any one (or more) section I've listed above. Say "I, Glkanter, would like the pro-Morgan POV in section blah blah blah to be eliminated by changing <something> to <something else>". Thank you. -- Rick Block (talk) 18:08, 13 January 2010 (UTC)

Sure. Right after you answer the subject of this section's heading, 'So, What Are The Significant Events, And Why, Of The Monty Hall Problem Paradox', with special emphasis on Morgan, who did not come up with the conditional argument. Or 'Is the Contestant Aware of a Host Bias?'. Or tell me how your 'FCC guy' answer relates to 'How Would The Equal Goat Door Constraint Benefit Huckleberry?', and how it's relevant to the MHP Paradox article. It seems you're more eager to write what you think I think, rather than what you think. Glkanter (talk) 18:25, 13 January 2010 (UTC)

Significant events:

1) Selvin publishes the problem in a letter to American Statistician., giving an unconditional solution. In a second letter Selvin responds to mail he's received suggesting he's wrong, clarifying his assumptions (the host knows where the prize is and chooses randomly if it comes up) and includes a conditional solution.

2) Others publish the same problem. It becomes a standard example of conditional probability in statistics textbooks.

3) vos Savant publishes a version in Parade, and defends her answer with an unconditional solution and then, in response to continued criticism, clarifies all of her assumptions except that the host chooses randomly if given the chance (and says nothing about conditional vs. unconditional)

4) Morgan et al. publish what is apparently the first peer reviewed paper on the problem, in American Statistician (no one has ever claimed this as far as I know, but I suspect it's not a coincidence that this is the same journal Selvin's problem originally appeared in), making the point that the problem is inherently conditional and criticizing vos Savant's solution/clarification as well as other unconditional solutions, noting that "The distinction between the conditional and unconditional situations here seems to confound many". The paper is fairly lighthearted since the problem has been well known in academia for years and is mathematically rather trivial. Since vos Savant ignored (or simply missed) the effect a potential host preference has on the player's chance of winning, the paper explores this specific aspect of the problem concluding that the player should switch regardless of any host preference (since the probability of winning by switching is between .5 and 1 even assuming a host preference). The conditional probability is 2/3 which is the same as the unconditional probability assuming the host picks randomly between two goats.

5) Gillman publishes a note (presumably without knowing about the Morgan paper) that says essentially the same thing as the Morgan paper

6) popular sources continue to publish unconditional solutions, saying the probability is 2/3 and (following vos Savant's lead) ignoring the issue of host preference and the distinction between the conditional and unconditional situations (which seems to continue to confound many).

7) numerous academic papers examine all aspects of the problem, ranging from what assumptions people make and how they understand it to esoteric variations (e.g. the quantum version)

8) the problem continues to be a standard example of conditional probability in many statistics textbooks. At least some (such as Grinstead and Snell) say the unconditional solution doesn't exactly answer the problem that is asked.

NOW will you please say how you're suggesting the "pro-Morgan POV" might be eliminated from any of the sections that you're complaining about? -- Rick Block (talk) 02:28, 14 January 2010 (UTC)

Imho you need to reverse 2) and 3) though, to my knowledge it mostly became a standard example in probability textbooks at large after the parade affair.--Kmhkmh (talk) 05:11, 14 January 2010 (UTC)

I think 2) should probably come after 4). Text books seem to use Morgan terminology. Are there any textbooks, making a big issue of the conditionality, dating before the Morgan paper? Martin Hogbin (talk) 10:05, 14 January 2010 (UTC)

What about 'Is The Contestant Aware Of A Host Bias' and 'How Can Huckleberry Do Better From Knowing The Equal Goat Door Constraint'? Glkanter (talk) 06:58, 14 January 2010 (UTC)

I thought you said "or". I'm getting the distinct impression you either don't have a suggestion or don't want to say what it is. Mediation will presumably help this. -- Rick Block (talk) 14:50, 14 January 2010 (UTC)

Once again, you spend more time on what you think I'm thinking than what you, yourself have to contribute. So, what about 'Is The Contestant Aware Of A Host Bias' and 'How Can Huckleberry Do Better From Knowing The Equal Goat Door Constraint'? These both demonstrate that Morgan, despite being published in the same journal as Selvin, has contributed nothing of value. But it's published, so it goes in. Glkanter (talk) 15:41, 14 January 2010 (UTC)

It's already in, in a way I'm comfortable with. I'm not the one saying the article needs to be changed in this regard. So are we OK here, or would you like to see it in, in some other way? And, if so, how? Again, I'm getting the distinct impression you either don't have a suggestion or don't want to say what it is. -- Rick Block (talk) 15:51, 14 January 2010 (UTC)

Well, what can I say, Rick? You put up an RfC/U on me for not editing the article often enough. Then I very lightly edit the article for clarity, and I touch off a near-edit war, and am accused of violating NPOV with the 2 'POINTy' dates I added to the headers. Then I tell you I look forward to being one of the consensus of editors, and you jump all over me for that. I've updated my concerns on the mediation request. They're consistent with my statements of 15 months now.

So, tell me how you intellectually justify Morgan's claims in light of 'Is The Contestant Aware Of A Host Bias?' and 'How Can Huckleberry Do Better By Knowing The Equal Goat Door Constraint?'? Glkanter (talk) 16:01, 14 January 2010 (UTC)

So your suggestions are at Wikipedia:Requests for mediation/Monty Hall problem#Additional issues to be mediated. Thank you. That's all I was asking for. These are concrete things we can work on (except for the "blather" comment). Regarding your questions - there is no reason whatsoever that I or anyone else should have to justify Morgan's claims to your satisfaction. They're published in a VERY reliable source backed up by similar (if not identical) claims made in other reliable sources. You apparently do not personally agree with them. Fine. Nobody says you have to. -- Rick Block (talk) 16:47, 14 January 2010 (UTC)

Door numbers matter

Consider the following game. Roll a (fair) dice, call the outcome X. Put as many white balls as the outcome in an urn and complete with black balls till 6 balls all together. Then before you draw a ball from the urn, predict its colour. Then draw a ball; if your prediction was right you win a car, otherwise a goat. What will be your prediction? Nijdam (talk) 17:04, 11 January 2010 (UTC)

I suggest that we continue this on the arguments page, I have copied your question there. Martin Hogbin (talk) 17:43, 11 January 2010 (UTC)

I have moved the 'Aids to understanding section'

I have moved the 'Aids to understanding section' to immediately follow the 'Popular solution section to see how it looks.

In my opinion it makes more sense there for the following reasons:

The section mentions nothing about conditional probability or the specific door that the host opens.

The article now has a logical sequence from simple to complicated.

The move does not affect Morgan's claim in the 'Probabilistic solution' section that conditional probability must be used.

Nobody who does not understand the basic problem is going to make and sense of the Morgan paper and subsequent discussions of conditional probability.

No doubt not everyone will like this but there seemed be be something of a consensus forming that it might be a better way to organise things. Note that I have not changed any wording, just moved a section, although I do notice many uncited claims and statements in the 'Aids to understanding section. This should be addressed regardless of the position of the section. Martin Hogbin (talk) 20:23, 13 January 2010 (UTC)

I strongly object to this, and as I've said think that it is not in keeping with WP:NPOV. We're going to talk about this in formal mediation (Nijdam has agreed). I'll file the request today. -- Rick Block (talk) 02:33, 14 January 2010 (UTC)

Why do you object? Have you read the article as it is now? It makes perfect sense and does not discredit the conditional solution in any way. If you could accept this change, which is just of order and not content, I do not think we would need mediation. I think most editors would be happy with the major content and structure of the article. I cannot see how moving the sections into a logical order without any other changes can be described as POV.

I do not know if you filed your formal mediation request in response to my action or not. I have agreed to it anyway. Remember that the mediator does not attempt to impose a view on us. My action was rather bold but it was a genuine attempt to bring this dispute to a close. The change it would be a major step in the right direction, if you could accept it. If not please give reasons. Martin Hogbin (talk) 09:58, 14 January 2010 (UTC)

I note that my change has been reverted with no reason other than to 'wait for mediation'. There is much support for this cgange and no logical reason against it has been proposed. These changes should be discussed here, as I am trying to do. Martin Hogbin (talk) 15:00, 14 January 2010 (UTC)

I said above I object on the basis of WP:NPOV. In more detail, this change presents the problem and then presents an unconditional solution as "the solution". The alternative conditional solution and the POV (of the sources we all know by now) that the unconditional solution does not exactly address the problem as they see it are buried in the article. This creates an "anti-Morgan" POV in the structure of the article. Unlike the Bayesian analysis, which is highly technical and arguably of little interest to a general readership, the conditional solution is well within the grasp of a general readership. Rather than bury this in the article I think we should actually go the other way and have a SINGLE solution section that presents both an unconditional and conditional solution. Per Wikipedia:Make technical articles accessible the marginally simpler unconditional solution should be presented first, but to comply with WP:NPOV I think an alternative conditional solution should immediately follow.

Regarding mediation - my impression is Glkanter wants mediation with or without this change. I filed the request in response to his continued insistence about this, not specifically because of this change. -- Rick Block (talk) 15:32, 14 January 2010 (UTC)

Formal mediation request filed

I've filed the request for formal mediation and informed all the users listed as involved parties, see Wikipedia:Requests for mediation/Monty Hall problem. If you are listed as an involved party please go to the request page and indicate your official agreement to participate in this process. If you think there are other issues to be mediated, please add them to the "Additional issues to be mediated" section. Wikipedia:Requests for mediation/Common reasons for rejection has some helpful comments that may be relevant. Thank you. -- Rick Block (talk) 03:01, 14 January 2010 (UTC)

Has Nijdam Invoked A 'Freeze' On MHP Article Editing?

His only comment I could find anywhere supporting his revert of Martin's edit was his edit comment 'Wait for mediation'. Does he have this unilateral power as an editor? Mediation might not be accepted, and we probably won't know for over a week. Interesting that his action immediately follows his agreement to take part in the Formal Mediation. Glkanter (talk) 14:18, 14 January 2010 (UTC)

He has as much and as little "power" as Martin or anyone else. The "normal" editing cycle is described at WP:BRD. If anyone makes a change that someone else reverts, the revert is a direct indication that this change does NOT have consensus. Making a change to "test the waters" is fine. Reverting such a change is fine. Reverting a revert is NOT fine. -- Rick Block (talk) 15:00, 14 January 2010 (UTC)

Consensus does not mean unanimity. There is, I think, much support for the change. I do not want to start edit warring but if there are no logical arguments presented as to why the change is wrong, I think it would be quite reasonable of me to revert again. I cannot see how changing the order of sections to make the article read better can be described as POV. I have given full reasons above as to why the change is an improvement. Why do you think it is not? Martin Hogbin (talk) 15:35, 14 January 2010 (UTC)

See above. -- Rick Block (talk) 15:39, 14 January 2010 (UTC)

If one doesn't want to wait for the mediation, than I can say I'm strongly against the proposed change. I want the "simple solution" directly being followed by the correct one, together with the critical notes about the simple solution, so anyone reading the article will guaranteed (I hope) see this. Nijdam (talk) 16:33, 14 January 2010 (UTC)

I would say that until the reader has understood the simple solution they have little chance of understanding the issues involved in conditional probability. In fact many readers will not be able to understand this anyway and many will not be interested. We cannot make our readers read something that they do not want to. The essence of the MHP is its simplicity. Martin Hogbin (talk) 17:00, 14 January 2010 (UTC)

Well, it's clear that keeping it the way it had been would be supporting Nijdam's pro-Morgan POV. We can't have that. Tell me Nijdam, how do you intellectually justify Morgan's claims in light of 'Is The Contestant Aware Of A Host Bias?' and 'How Can Huckleberry Do Better By Knowing The Equal Goat Door Constraint?'?

What we can't have is POV is either direction. You apparently think the current article has a pro-Morgan POV. The fix for this cannot be to make it POV in the other direction. A mediator might help us reach a better solution. -- Rick Block (talk) 18:18, 14 January 2010 (UTC)

Nijdam wrote, "I want the "simple solution" directly being followed by the correct one..." He gives no other reasons. I think it's correct to classify his justification solely as pro-Morgan. You've made similar POV conclusions based on a whole lot less. Glkanter (talk) 18:35, 14 January 2010 (UTC)

And maybe you could clarify for us exactly what you and Boris resolved before he left the discussion? Glkanter (talk) 17:12, 14 January 2010 (UTC)

I would also ask Nijdam to prove on the arguments page that any method of solving the symmetrical problem that does not involve conditional probability must be wrong. Martin Hogbin (talk) 17:21, 14 January 2010 (UTC)

IMO, these questions are asking for WP:OR. It doesn't matter what Boris and Nijdam resolved or whether or not Nijdam can prove anything. The only thing that matters is what reliable sources say. You and Glkanter seem to be having a great deal of trouble with the basic concept of saying what reliable sources say without injecting your own POV. This is another issue a mediator might help with. -- Rick Block (talk) 18:27, 14 January 2010 (UTC)

Please, Rick. You've posted on these pages for what, 6 years now? I've read plenty of your personal interpretations and offers to try various game simulations and slightly different problems. There's a difference between Wikipedia policies and intellectual honesty. And there's a difference between how an article is edited and what good faith editors discuss on talk pages. Glkanter (talk) 18:35, 14 January 2010 (UTC)

What there's a difference between is trying to help people understand what the article says (which I've done plenty of) and suggesting edits based on whether or not an editor can "prove" something (which is what you and Martin seem to be doing). The latter has no place in Wikipedia. Edits are based on what reliable sources say, not on what editors can prove. Again, I think this is an issue a mediator might help with. -- Rick Block (talk) 18:50, 14 January 2010 (UTC)

Nijdam and you are the ones asserting that an unconditional solution must always be wrong, you must therefore prove this. There is one reliable source which makes a similar claim (for their interpretation of the question) but as I say below, there is another source which says that they might have misunderstood the question. Martin Hogbin (talk) 18:57, 14 January 2010 (UTC)

My interpretation is that Nijdam is asserting his personal view here, and on the /Arguments page, that the problem is inherently conditional. Although his view matches that of some of the sources, I don't think he's insisting the article take this as its POV. It's not supposed to matter but you are aware that he's a professor of mathematics (right?). I'm asserting there are multiple reliable sources that say the unconditional solutions don't exactly address the Parade version of the problem statement and want (insist) the article fairly represent this POV. -- Rick Block (talk) 21:37, 14 January 2010 (UTC)

Face the facts, Rick. In a peer reviewed journal, Morgan claims all the simple solutions are false. That's the entirety of Morgan's contribution to the literature. Morgan's paper has many flaws, including misquotes and math errors (you could ask Nijdam about this aspect), has a disclaimer from Seymann attached to it, and his claim has not been acclaimed by the professional community in the 19 ensuing years. Plus, it's inconsistent with the problem statement, 'Suppose you're on a game show...' What's left? The peer-reviewed journal part? How is the fact that it is in a peer reviewed journal of any utility or interest to the Wikipedia reader? It's published. It goes in. Why not chronologically? Glkanter (talk) 18:47, 14 January 2010 (UTC)

Rick, this seems to be the line that you resort to when you are beaten in logical argument. As you well know, there are plenty of reliable sources that treat the problem unconditionally, there are also reliable sources which treat it conditionally. There is one source (Morgan) that suggests that the unconditional treatment is incorrect, there is one, equally reliable, source (Seymann) that suggests that Morgan may have misunderstood the question. All these sources are, quite rightly, reflected in the article. Our job as editors is to decide the best way to do this, for the benefit of our readers. No source tells us how to do that. Martin Hogbin (talk) 18:51, 14 January 2010 (UTC)

This is the line I resort to when it becomes obvious further logical argument is pointless. The fact is many sources, not just Morgan, say the problem as it appeared in Parade asks a conditional probability question and that unconditional solutions are not directly responsive to this question. Our job as editors is to insure the article is written (per WP:NPOV) "from a neutral point of view, representing fairly, proportionately, and as far as possible without bias, all significant views". No source tells us how to do that, but since you personally "hate" (your quote above, and your "criticism" page, etc.) the Morgan et al. paper you have a clear bias. Of course this doesn't necessarily mean you can't edit in an unbiased fashion, but you do seem to be having trouble with this. Yet again, I think this is an issue a mediator might help with.-- Rick Block (talk) 19:18, 14 January 2010 (UTC)

Nijdam reverted Martin's 'Aids to Understanding' placement edit solely because of his pro-Morgan POV and bias. He wants the allegedly only 'correct' answer encountered by the reader as soon as possible in the article. That violates NPOV. Badly. Glkanter (talk) 19:06, 14 January 2010 (UTC)

Is it his statement (that this is the only correct answer) that you are saying violates NPOV, or his edit? As long as he doesn't edit the article to say or imply the conditional solution is the only correct solution he's free to think whatever he wants (as are you). We all have our own personal POV. What NPOV says is we have to make sure the article doesn't have a POV. This is something else I think a mediator might help with.-- Rick Block (talk) 19:41, 14 January 2010 (UTC)

I am happy to try mediation but please remember that it is not the mediator's job to enforce rules or decide who is right. They can only help us to agree amongst ourselves. Martin Hogbin (talk) 20:23, 14 January 2010 (UTC)

Right. A mediator would also help us communicate (would, in fact, probably lay down some pretty strict rules about how we should say things and interact with each other) and presumably would be happy to explain relevant policies and guidelines. My impression is Glkanter is not happy with my attempts at explaining policies. -- Rick Block (talk) 21:37, 14 January 2010 (UTC)

Glkanter will express again that you should spend less time thinking and conjecturing and writing about what I'm thinking. I'm not shy about letting you all know what I'm thinking. Glkanter (talk) 22:21, 14 January 2010 (UTC)

I'm sorry, but I find getting a straight answer out of you for what seem to me to be simple direct questions (for example, per the thread somewhat above where you insisted I answer certain questions before you would deign to respond) to be nearly impossible. I sincerely hope a mediator can help us communicate. -- Rick Block (talk) 23:27, 14 January 2010 (UTC)

Martin made an edit and explained his non-POV reasons why. Nijdam reversed it giving ONLY his Morgan-POV reason shy. Seems clear to me where NPOV is being violated. Strange that you can't see that, Rick. Glkanter (talk) 20:53, 14 January 2010 (UTC)

We all know you're being snide here. Please stop it. This is something else a mediator could help with. -- Rick Block (talk) 23:27, 14 January 2010 (UTC)

Yes, Rick. Quoting people in context is 'snide'. And dates are 'POINTy'. And we continue to disagree on nearly ever topic broached in the last 15 months on these talk pages. Glkanter (talk) 02:03, 15 January 2010 (UTC)

To clarify, what I'm referring to as snide is "Strange that you can't see that, Rick". -- Rick Block (talk) 03:28, 15 January 2010 (UTC)

Let us give it a try, but remember, both sides will have to give something to reach a consensus, mediator or not. Martin Hogbin (talk) 23:37, 14 January 2010 (UTC)

Logical and scientifical solutions

The popular solution is actually a logical solution, while the probabilistic solution is a scientific solution. It is quite clear that within science several sources explicitly state the problem to be conditional and therefore the unconditional to be wrong, while no scientific source states the opposite (including Seymann). Some scientific sources used logic in fact, and were corrected by their colleagues. They did not respond to that, nor did any of them criticize the conditional approach.

The 'conditional' scientists all corrected their colleagues, because the latter were not practicing pure science, even though they may have been fully right logically. The problem with the last option is that logic just can't be proven. although logical sources have certain reliability too. I don't see any other possible interpretation.

This is yet another attempt to agree on this matter, because as I said before, we are all right basically. There is no wrong or right, but within disciplines. Logic can only be beaten logically, while science can only be beaten scientifically. They are both as well superior as inferior to another, and this very extreme paradox cannot simply be positioned objectively. Heptalogos (talk) 22:20, 14 January 2010 (UTC)

What does "The problem with the last option is that logic just can't be proven." mean? It sounds like it contradicts the academic teachings of 'logical proofs'. Glkanter (talk) 22:26, 14 January 2010 (UTC)

When so called logic is proven, it becomes law. Any logic outside the law is unproven. As a result, no proven logic exists. Suppose you use logic to create and claim law. The law should be defined as generally true (provable), to some degree. However, when the law is proven, there is no automatic proof for the logic behind it. Unless you use the same logic to create several proven laws. "The same logic" must then be clearly defined and becomes law.

Some principles may be or seem so clearly logical, but not existing as law (yet). On the other hand, as they don't exist as law, are they really that logical? At the moment, there is no law on practicing conditional solution other than to use any exact given information as a condition. Even if all intelligent people in the world would agree on a specific exception, as logically true, it's not scientifically true. These people could maybe create and claim a new general law, which may be proven, after which even the most consequent scientists will agree on this 'logic', but only because it has become law. And they are right, not beaten, because they're still being as consequent as they should, scientifically. So these are really different dimensions. Heptalogos (talk) 08:49, 15 January 2010 (UTC)

The discussion between Morgan and Marilyn didn't make any sense. They were in different dimensions. Their argue is one of historic value! Most famous paradox, most intelligent person, and most consequent scientists ever. It may be a pitty that the original paradox has been kidnapped for this, but on the other hand this 'new issue' is what it made even bigger. So I think both issues really deserve a prominent position in the article, as long as we can clearly separate them, starting of course with the original paradox. Heptalogos (talk) 09:40, 15 January 2010 (UTC)

Something else to add to the mediation list

One of the points of the three fundamental content policies (WP:V, WP:OR, and WP:NPOV) is to avoid the sorts of arguments that have been raging on this page and the /Arguments page. In total, what these policies mean is all we need to agree on is what sources are reliable (WP:RS makes that pretty easy), whether these sources say what we respectively are claiming they say (nothing too difficult there), and how much weight to give what each source say. That's it. The first two should be easy as pie (alright, maybe easy as pi) since whether we agree with what any of the reliable sources say shouldn't even come up. We simply need to agree whether the article is representing what the sources say "fairly, proportionately, and as far as possible without bias" (this quote is from WP:NPOV). The last one (weight) is trickier and sometimes leads to heated arguments. On this page, we've mostly been arguing about the stuff that is supposed to be EASY. I hope mediation will help this, although I fear that the discussion will then morph into a heated discussion about how much weight we should give specific sources. Assuming mediation happens, while we're there we should make sure we explicitly address the weight issue as well. -- Rick Block (talk) 04:13, 15 January 2010 (UTC)

Rather than wikilawyering we should concern ourselves with the overriding objective to improve the article, for the intended readership, which is a wide section of the general public. Although we are entitled to WP:ignore the rules to improve the article, I am not necessarily suggesting that we do that, just that the rules should not in any way direct us to write the article in a way that will not be useful to most of the general public. Martin Hogbin (talk) 10:48, 17 January 2010 (UTC)

Martin - you are at least implying the article can violate WP:NPOV if doing so would make it more useful to most of the general public. IMO, you are completely wrong about this. I would say if we can't write an article that is both useful to the general public and complies with NPOV we are simply incompetent editors, but if we have to pick one we have to pick NPOV. From WP:NPOV: The principles upon which these policies [NPOV, OR, and V] are based cannot be superseded by other policies or guidelines, or by editors' consensus. -- Rick Block (talk) 17:50, 17 January 2010 (UTC)

N, I am not suggesting we abandon NPOV, although, in the end, everything on WP, including policies, is decided by consensus. The question we have to address is the exact interpretation of those policies and my suggestion is that we do this in order to meet the fundamental purpose of WP which is to inform. Martin Hogbin (talk) 11:24, 18 January 2010 (UTC)

"Wikilawyering", I love it. They've seen it all, haven't they? In my opinion, some good things came out of the discussions of the last couple days:

1. The real items for mediation have made themselves known. How much weight to give Morgan, and is the 'host bias' conditional problem statement consistent with the information given in either Selvin's or Whitaker/vos Savant's MHP?

2. All those "let's start fresh and try to make a compromise article" attempts were destined to fail.

3. Rick's threats of the consensus "violating NPOV" were bluster, unsupported by Wikipedia policy.

Glkanter (talk) 13:20, 17 January 2010 (UTC)

Your point #1 is half right. One of the issues is how much weight to give the viewpoint expressed by Morgan et al. However the second half of this ("is the 'host bias' conditional problem statement consistent ...") is not for us to decide. Sources have decided this. And, for many many sources the decision is clear. I have no idea what you're talking about with your second point. Regarding your third point: I have made no threats, "the consensus" is not a group of people, and this point is yet more low level harrassment directed my way entirely consistent with the objectionable behaviors described here. Please just stop it. -- Rick Block (talk) 17:50, 17 January 2010 (UTC)

The problem of NPOV in MHP

It is NOPV to chronologically:

• Start with the original paradox and explain it fully, logically as well as mathematically.
• Describe the complex issues within science to solve particular statements.

It is also NPOV to:

• Start with the most famous particular statement of the MHP, which is from Parade.
• Explain this one logically as well as mathematically.
• Which will at the mathematical solution already start the complex issues, because of the particular Parade statement.

So, how do we solve this? Heptalogos (talk) 10:11, 15 January 2010 (UTC)

For practical reason, I think we all agree on the Parade statement to start with? A problem description is initially needed, reflecting a mundane situation, instead of basic formula. Any mundane problem description should come from reliable sources and be significant. So without an alternative, there's not much of a discussion here. Heptalogos (talk) 10:31, 15 January 2010 (UTC)

As the Parade statement is particular in a certain way, the mathematical solution has an enormous tail of complexities. What if we do it like this: logical explanation of the paradox first, as it is now. Next the mathematical solutions, again the same, but this section not being significantly bigger (in text) than the logical section. Because that would not be NPOV either. This section should preferably describe the unconditional and conditional scientific solutions, and mention the issue of scientific consensus in favour of the conditional method. Then it may direct to a lower section in the article to give a full description of all scientific sources and arguments. This seems to me as a reasonable compromise, because Nijdam is justly being served at the issue of common readers being aware of the essential criticism on the unconditional method, while Martin and Glkanter are being served at the issue of having the "aids to understand" section above all detailed sources and arguments of science. Heptalogos (talk) 10:51, 15 January 2010 (UTC)

This is exactly the structure I favor. Further, I don't see any particular reason to separate the "logical" solution and the "scientific" solution into different sections. It doesn't seem to me to be that difficult to do both in one section per the proposal above (see #Proposed unified solution section). For a time, I thought there was good progress being made on that solution. -- Rick Block (talk) 15:19, 15 January 2010 (UTC)

This does not address the problem that will be raised for the vast majority of our readers. As Glkanter has pointed out, none of the thousands of letters that vos Savant received was concerned with which door the host opened, they were all about why the answer is not 1/2. This is the question that we must answer first. Martin Hogbin (talk) 15:33, 15 January 2010 (UTC)

Rick, I don't like the unified solution because it spends only a few lines on the paradox that confuses so many people and is then already starting to mention Morgan et al. The scientific solution is very complex, which is the reason to describe it separately. Heptalogos (talk) 19:53, 15 January 2010 (UTC)

Martin - even in the unconditional case you have to talk about the door the player picked, the door the host opened, and the other door. You might as well call these "door 1", "door 3", and "door 2" (respectively). Do you want to add "for example" before every door number to clarify that the initial unconditional solution is only using door numbers as examples (which, btw, is true of the conditional solution as well)? Player picks door 1, host opens door 3, and player can now switch to door 2 is used as the representative example of the general case in nearly all sources. You seem to be saying that using the door numbers in this solution means we're limiting the response to only those players who have picked door 1 and have seen the host open door 3. This is not what ANY of the sources who discuss the solution in terms of these door numbers are intending. Your refusal to see this point mystifies me.

Your table (#Discussion and proposals aimed at reaching a compromise on this subject) is incredibly confusing. Why are there two identical columns for "you choose a goat"? You don't KNOW what you chose. What you initially know is the car is behind your door, or one of the other two doors, and then you find out the car is NOT behind the door the host opens. So, you start with 3 doors (not car, goat, goat - for example, what if rather than goats the losing doors are simply empty?). This model (door centric, rather than car/goat/goat centric) is exactly the basis of vos Savant's case analysis solution (go look at it). This approach matches the example in the problem description (yours doesn't).

I am incredibly tired of arguing about this. How about if we start talking exclusively about how sources handle this. My claim is the unconditional case is handled by vos Savant and nearly all other popular sources using the door numbers given as examples in the problem statement. If you'd like to argue whether this is what popular sources do or not, we can presumably put together a list and go look. Would you like to offer up a source that does not use door numbers? -- Rick Block (talk) 18:29, 15 January 2010 (UTC)

I am not sure exactly what Heptalogos is suggesting. The order I want is U/C solution, Aids to understanding, C solution, Causes of confusion, Variants etc. Martin Hogbin (talk) 15:36, 15 January 2010 (UTC)

I am suggesting about the same as you do, while also offering a comment, within the U/C section, about scientific consensus in favor of the conditional approach. Apart from that I think it's better to replace U/C by L/S meaning logic/scientific. Heptalogos (talk) 19:53, 15 January 2010 (UTC)

No, Martin is disagreeing with you. He wants an initial section that only discusses what you're calling the Logical solution with no mention of conditionality and no mention of scientific consensus, and then an entire section on "aids to understanding" this "logical" solution, and only then a section on the "scientific" solution. -- Rick Block (talk) 21:27, 15 January 2010 (UTC)

It's about the same. He also doesn't want the Morgan battle in between the logical solution and the aids to understand it better. But then again I agree with you that the conditional (scientific) approach should really be mentioned and explained basically right after the logical approach (NPOV), but with a reference to another section to go in detail. Heptalogos (talk) 21:45, 15 January 2010 (UTC)

Unfortunately, we cannot have it both ways, or everyone would be happy and there would be no argument. I want the 'Aids to understanding' section to follow the simple solution section. This is not to intentionally downgrade the conditional solution but simply because most of the reader's difficulties in understanding will be with the simple solution, just as it was for vos Savant. People insisted that the answer was 1/2, not that the host goat door choice was important. Martin Hogbin (talk) 00:12, 16 January 2010 (UTC)

Please read through the current 'Aids to understanding' you will see that it refers only to the issue that I have described above. There is no mention of the host's choice of goat door. Martin Hogbin (talk) 00:15, 16 January 2010 (UTC)

I know what you want, but others also have justified wishes. So what is specifically wrong with the compromise that I propose? Heptalogos (talk) 09:52, 16 January 2010 (UTC)

Summary

See Talk:Monty Hall problem/Arguments. Nijdam (talk) 14:34, 15 January 2010 (UTC)

Let's Discuss, As Per Rick's Comment On Wikipedia Policy, How Much 'Weight' Each Source Receives In The Article

I love this topic! It's what I've been arguing about for months. Sure, Morgan is published in a peer reviewed journal. So what? What do they have to say that's new? The article has at least three gaping errors. Only with the errors can they make the contrived claim that all simple solutions are false. I wonder, even ones that hadn't been published yet?

Here's Rick's diff.

How about Selvin? I added '1975' to the Popular solution section. Someone pointed out that Selvin's 1975 paper isn't even referenced there. And his conditional paper of the same year isn't in the Probabilistic solution section.

This is what real life editors do! They 'weigh' the newsworthiness of various articles from various sources. And they discuss it. With ideas, and logic, and facts.

So, perhaps more Selvin, and less Morgan POV? Glkanter (talk) 18:50, 15 January 2010 (UTC)

I would suggest we wait until mediation for this because it is going to immediately get into Wikipedia policy issues that I think would be best explained by someone you would perceive as a neutral party (i.e. not me). I will say that this is an area that takes editorial judgment, which means it's not nearly as black and white as "is X a reliable source". -- Rick Block (talk) 19:29, 15 January 2010 (UTC)

You may choose to participate or not, Rick. I'm sure there are others like me who will get bored waiting another week or so. Now that you agree 'weight' does not equate to 'biased POV', we can have this discussion again.

So, we can talk about how to edit the article, and actually edit it, or we can offer more urns puzzles, formal probability notations, and narratives on 'truth'. Or, some may wait for the mediator. Glkanter (talk) 19:50, 15 January 2010 (UTC)

Morgan's weight:

• Very explicit arguments against many (unconditional) methods used so far. (are they the first?)
• Very explicit arguments against the method Vos Savant is using. (are they the first?)
• Very first attempt to solve the problem without making assumptions. (are they the only ones?)
• 'Scientifically' published and peer reviewed. (did any unconditional solution?)
• The only scientists to have an extensive debate with Vos Savant.

About the errors: that's POV and it doesn't even really matter in the weight issue.

Please suggest something about Selvin 1975. Do you have his letters? Heptalogos (talk) 20:11, 15 January 2010 (UTC)

The errors are not POV. They are real. The paper discredits itself. Misquotes, math errors found by Martin and Nijdam, treating the host and the car placer differently, assigning 'bias' and transferring this to the contestant on a game show... Much like 'the Earth is flat' doesn't get much emphasis, neither should 'the host, but not the car placer, has a bias known by the contestant' Glkanter (talk) 14:44, 16 January 2010 (UTC)

I think before anyone can talk about this, they need to go read WP:WEIGHT. Weight and POV are different, but related, issues. -- Rick Block (talk) 21:24, 15 January 2010 (UTC)

Certainly. Why your comment? Heptalogos (talk) 21:49, 15 January 2010 (UTC)

Because we all need to able to talk about the issues that will come up using the same terminology. The appropriate weight relates to (from the link I provided) "prevalence in reliable sources, not its prevalence among Wikipedia editors or the general public" (emphasis in the original). Weight also relates to viewpoints as opposed to specific sources. These are things I'm fully expecting to argue with Glkanter and Martin about, but I want there to be a shared understanding of what weight means before we start arguing specific issues (or else I will certainly be accused of "filibustering" or trying to subvert the will of the masses or whatever).

I would truly prefer to defer this discussion until we're in mediation so that I don't have to both help people understand Wikipedia policy and also argue one "side" of this. Doing this apparently tends to make the policy clarifications sound like partisan arguing. -- Rick Block (talk) 23:59, 15 January 2010 (UTC)

OK, I understand. I was basically trying to convince Glkanter personally about the significance of Morgan, nothing more. But I can define the same arguments a little bit different to present the viewpoints in proportion to the prominence of each in the sources. First of all I think Morgan is mentioned a lot in other reliable sources, while it's already most reliable because it was published within scientific media. Then they spent much energy in disproving others, including Vos Savant, on which they published another article. Another (the) prominent part in their main article is their solution without assumptions. The only aspects now missing are Morgan being the first ones, which is probably indeed not relevant, except for Glkanter and myself personally.

I don't see the problem of you switching roles as soon as mediation starts. Is there any Admin responsibility conflicting with that? Heptalogos (talk) 10:55, 16 January 2010 (UTC)

There is no actual conflict. Anyone is free to try to clarify Wikipedia policies during a discussion (although this sometimes leads to Wikipedia:Wikilawyering). As far as content disagreements are concerned admins have no more and no less authority than anyone else - specifically admins can't take administrative actions to enforce their preference of content, i.e. cannot block users or protect a favored version of an article. What I would like is for policy issues to be brought up by an acknowledged neutral party, and thus keep the "meta" (policy) issues distinct from any conflict we might have about content. -- Rick Block (talk) 18:07, 16 January 2010 (UTC)

Regarding a couple of questions raised above. Glkanter asks about Selvin's letters. These letters to the editor (they're not "papers") are referenced in the "History" section. They're not referenced elsewhere since they are being treated here as primary sources. Please see the first bullet at Wikipedia:Reliable sources# Scholarship.

Heptalogos asks

• Is Morgan et al. the first to explicitly argue against many (unconditional) methods used so far? I believe so.
• Is Morgan et al. the first to explicitly argue against the method vos Savant uses? I'd say they were technically the first, although Gillman is effectively simultaneous (the Morgan et al. paper was published in November of 1991, Gillman's in January of 1992).
• Is Morgan et al. the only attempt to solve the problem without making assumptions? Specifically meaning not making assumptions about the host preference between goats, Gillman approaches the problem in exactly the same way. This same approach is one of several presented by Krauss and Wang. At least several others (all presumably assuming initial random car placement) show the same result, i.e. the chance of winning by switching given a host preference p for the door that has been opened (meaning the host opens this door with probability p if there are two goats to pick from) is 1/(1+p).
• Are any unconditional solutions "scientifically" published and peer reviewed? I'm not sure exactly what you mean by this, but assuming you mean a source that acknowledges the difference between the unconditional and conditional questions and then uses an "unconditional" solution to rigorously address the conditional case (like Gill's WP:OR, below) I don't know of such a source.
• Are they the only scientists to have an extensive debate with Vos Savant? I believe the sense of what you're saying is true, although "extensive debate" seems like an overstatement. They published a paper. She wrote a letter to the editor in response. They published a rejoinder.

As mentioned in the "History" section, Barbeau's book contains a survey of the academic literature through about 2000. He published an earlier version of this survey in 1993, it's the Barbeau 1993 reference in the article. -- Rick Block (talk) 20:31, 16 January 2010 (UTC)

Thanks for the answers Rick. Those are the exact answers I was aiming for. Heptalogos (talk) 22:40, 16 January 2010 (UTC)

Do any of these sources criticize the simple solutions based only on the information given in the various forms of the problem statement? Or do they all contrive a 'host preference', then criticize the simple solution for not solving this different problem? Do any of them also contrive a 'car placer preference'? Glkanter (talk) 21:37, 16 January 2010 (UTC)

I've provided quotes from Morgan et al., Gillman, and Grinstead and Snell before (see above #What If Morgan Had Used A Different Variant?) - what they're all saying is that the "simple" (unconditional) solutions don't address the problem as they interpret it, so yes they are criticizing these solutions based on the problem statement. The fully conditional solution in Grinstead and Snell accommodates a 'car placer preference' although they (explicitly) assume the initial car placement is random. These sources don't "contrive" a host preference but say the probability of winning depends on it, and if you don't know what this preference is or don't assume a value for it you can't exactly say what your probability is of winning by switching. Krauss and Wang include a discussion of this as well. They consider the "two door scenario", where the door the player picks as well as the door the host opens are given, to be the "standard version" and say "... one has to make assumptions about what Monty Hall would do in A1 [the case where the player has initially picked door 1 and the car is behind door 1] and estimate the probability that Monty Hall would open Door 3 rather than Door 2." -- Rick Block (talk) 23:55, 16 January 2010 (UTC)

Do any of these sources reason why they do assume e.g. random car placement (etc.), but not random host behavior? Heptalogos (talk) 11:23, 17 January 2010 (UTC)

Morgan et al. are clearly trying to match vos Savant's assumptions - they even call it the "vos Savant scenario". She (and they) assume initial random car placement, that the host always opens a door revealing a goat, and that the host always makes the offer to switch. They mention at the end of the paper that it would also be possible to consider non-uniform probabilities of car placement. Assuming they overlooked or ignored this case is (IMO) simply willful misinterpretation of what they wrote.

Gillman restates the problem (does not quote the Parade version) and explicitly states the initial car location is to be taken as random.

Grinstead and Snell quote the Parade version as reprinted in vos Savant's book "Ask Marilyn" (I haven't checked whether their quote matches this version - what they quote is definitely not the same as the original Parade version) and explicitly say (without rationale) they're assuming the car is initially located randomly.

One might surmise that making this assumption focuses the problem on the effect of the host opening a door. By making this assumption, the probability before the host opens a door is clearly 1/3 and the question becomes what is the probability after the host opens a door. For editing purposes, my claim is we don't care why this assumption is made. The fact is this assumption is made. If the sources don't say why, then the article can't say why and, unless there are other sources that explain or question this assumption, the article can't either. -- Rick Block (talk) 21:04, 17 January 2010 (UTC)

Rick, very clear, thank you. It's quite a mess. However, it triggers me to find the exact relations between sources. Heptalogos (talk) 11:58, 18 January 2010 (UTC)

How Richard Gill110951 sees things now

I distinguish three Monty Hall problems, and I think they are all legitimate problems to discuss; they have all been discussed in the literature of brain-teasers, mathematics, psychology...

There is no law saying that exactly one of these three is "the" Monty Hall problem

Here they are:

0: Marilyn vos Savant's question "would you switch?"

1: A mathematician's question "what is the unconditional probability that switching gives the car?"

2: A mathematician's question "what is the conditional probability that switching gives the car?"

Please specify the sources for 1 and 2, otherwise there's no use in discussing it here. Heptalogos (talk) 11:31, 16 January 2010 (UTC)

Whitaker. Sorry, misread the comment above. I agree that Whitaker should be interpreted as 0. Martin Hogbin (talk) 15:02, 16 January 2010 (UTC)

The following analysis gives the right answers to the questions 1 and 2 under the assumptions conventionally thought to be appropriate. I use Boris Tsirelson's beautiful trick ("symmetry") to deduce the answer to question 2 from the answer to question 1. I finally make some comments on question 0.

My set-up:

The quizteam hides the car, the player chooses a door, the quizmaster opens a door.

Three random variables taking values in {1,2,3}.

I don't care what your interpretation of probability is (subjective or frequentist or ...).

I don't care (for the time being) whose probabilities we are talking about at which stage of the game.

Notation:

C = door where Car is hidden

P = door first chosen by Player

Q = door opened by Quizmaster

Assumptions: with certainty,

Q unequal to P

Q unequal to C

Because of the first assumption we may define

S = door which follows by Switching = unique door different from P and Q

1) Short solution to problem 1:

If Prob(P=C)=1/3 then Prob(S=C)=2/3, since the two events are complementary.

2) Short solution to problem 2:

In this problem, the door chosen by the player is fixed, P= x, say.

We are to compute Prob(S=C|Q=y) for a further specific value y unequal to x. Let y' denote the remaining door number, besides x and y.

Assume that (given the chosen value of P), C is uniform, and the distribution of Q given C is uniform.

So by assumption Prob(P=C)=1/3 and therefore as in Problem 1, Prob(S=C)=2/3.

The latter probability is the weighted average of the two probabilities Prob(S=C|Q=y) and Prob(S=C|Q=y'), weighted by the probabilities Prob(Q=y) and Prob(Q=y').

Since the distribution of C gives equal probabilities to y and y' and since Prob(Q=y|C=x)=Prob(Q=y'|C=x)=1/2, nothing is changed by exchanging y for y' and vice-versa.

Thus the two conditional probabilities Prob(S=C|Q=y) and Prob(S=C|Q=y') are equal, and equal to their (weighted) average 2/3.

0) Short solution to problem 0.

I don't know what strategy the quizteam and quizmaster use, so naturally I had chosen my door uniformly at random, independently of the car's actual location.

Since I know game theory I know that "always switching" is the minimax strategy. It guarantees me a 2/3 (unconditional) chance of winning the car.

I don't care a damn what my conditional probability of winning is, given my specific initial choice: say door 1, and the quizmasters' specific choice: say door 3.

I don't know this probability anyway, since I don't know the strategy used by quiz-team and quiz-master.

I only know that Monty Hall always opens a door revealing a goat.

Gill110951 (talk) 11:03, 16 January 2010 (UTC)

This belongs on the arguments page. Heptalogos (talk) 14:12, 16 January 2010 (UTC)

Gill, I have shown much the same thing on my analysis page using fixed door numbers.

What is your opinion on the order of sections within the article? I would like to see the 'Aids to understanding' immediately follow the 'Popular solution' section as this is the section that most people cannot understand. Martin Hogbin (talk) 15:08, 16 January 2010 (UTC)

@Gill: as I wrote in my mail, once the problem is well stated, the soluton is (must be) obvious. Now your points 0, 1 and 2 do not clearly state the problem. I will ask you to go to the arguments page under Talk:Monty Hall problem/Arguments#Summary, where I also tried to formulate the different views on the MHP, and specify your versions 0, 1 and 2, and if possible relate them to my versions A, B and C.Nijdam (talk) 11:29, 17 January 2010 (UTC)

@Nijdam, @Martin, @Heptalogus, thanks for your comments. Let me explain what I am trying to do here. Problem 0) is supposed to be the question exactly as posed by Marilyn vos Savant, i.e., in her own words. Problems 1) and 2) are what people around here call the unconditional and the conditional problems respectively. They are two different ways in which mathematically inclined people have converted Marilyn's verbal problem into a formal mathematical problem. For each of the three problems the solution is immediate. I wrote it down in explicit, respectable mathematics (especially after I cut a lot of crap out of my first try at problem 2). The point I am trying to make is that Marilyn vos Savant asked whether or not one should switch doors, NOT what some probability was. Her problem was not a maths problem. It is only if you decide that the right way to make your final choice of door is by computing a probability, that you arrive at problems 1) and 2) - the "conventional" unconditional and conditional variants of the problem, which people spend their time here fighting about. I think that, if you think Marilyn is asking you for a probability, then whether 1) or 2) is closer to the question she is asking is a question of interpretation of American-English idiom. Did she refer to the actual door numbers painted on the doors in advance of the show, or did she mean that we decide to call the door which the player chooses "door 1"? Anyway my point is, she did not ask for a probability, she asked for a strategy. The usual *solution* to the conditional problem, problem 2, requires one to make all kinds of assumptions which are not justified by the problem as originally phrased. However, lots of people have talked about it, so it should be on wikipedia, since we are not supposed to be presenting *our* opinion as to what the MH problem ought to be, but merely writing down what it has been to various people. My own humble opinion is that the most satisfactory treatment of the problem uses the language of game-theory, i.e., we explicitly take account of any strategy which might be used by the quiz-team & quiz-master. We don't make unwarranted assumptions about it, whose raison d'etre is merely that they are designed to deliver the answer 2/3. Gill110951 (talk) 20:52, 17 January 2010 (UTC)

Gill, I completely disagree with you about game theory, this, in my opinion adds further complicationto an already difficult problem. If you want to discuss that further, I suggest that we do so on the arguments page. Martin Hogbin (talk) 21:01, 17 January 2010 (UTC)

Gill, I completely agree with you about game theory. If you want to discuss that further, I suggest that we do so on the arguments page, until you come up with a reliable source suggesting this method to solve the MHP. Heptalogos (talk) 22:26, 17 January 2010 (UTC)

I spoke to some game theorists who said they "know" the game theoretic solution to the Monty Hall problem. And any way, it really *is* an easy exercise after you have done Game Theory 101! Probably there exists a published discussion somewhere. Sometime I will post a combination, and condensation of my notes so far (see references Gill 2009a, 2009b, and since an hour ago also **** 2010 ****) to arXiv.org and submit to a light-weight but respectable peer-reviewed journal (more respectable than the American Statistician). BTW I think that Morgan et al. is a very poor paper. It is solving a Statistics 101 problem in a pompous and arrogant way, as well as being definitely un-scholarly in being dogmatic about their version being "the" version; for which purpose they even misquote earlier works. In the meantime my job is to go on looking for reliable sources, creating reliable sources if necessary, and learning from what people say here. In particular I must check what wikipedia already has on game theory. Game-theory ought to be more accessible and more well-known. Personally, I find a game-theoretic approach illuminating. In fact I find it essential since it is the only way as far as I know to give a decent argument for always switching, whatever the conditional probabilities..., without making articial assumptions about the quizmaster. @Martin and @Heptalogus, I am happy to discuss this with anyone, anywhere they like, I have tried to provide information which anyone can use to figure it out for themselves. Anyone who wants to erase anything I put on wikipedia can go ahead. No problem. Gill110951 (talk) 18:01, 18 January 2010 (UTC)

Game Theory 101: von Neumann's (1928) minimax theorem. References:

The minimax theorem (von Neumann, 1928), http://en.wikipedia.org/wiki/Minimax_theorem#Minimax_theorem

Von Neumann's seminal contributions to game theory: http://en.wikipedia.org/wiki/John_von_Neumann#Economics_and_game_theory

What game theory is nowadays: http://en.wikipedia.org/wiki/Game_theory

Honestly, I don't think that the minimax theorem complicates matters. It simplifies matters because we know there is a minimax solution and once we have guessed it, it is easy to check that we were right. And the two party's minimax strategies are exactly the player's and the quiz-master's "symmetric" probability distributions, used to randomize their choices. The probability distributions which turn up all over the place on these pages.

Gill110951 (talk) 19:45, 18 January 2010 (UTC)

I have no objection at all to a section about game theory and the MHP. What I would not want to see is game theory replacing the simple solution of the problem in which the car placement, the player's initial choice, and the host's legal door choice are all assumed to be uniform at random, as is the standard in mathematical puzzles.

After the discussion about the affect of a known or suspected host door opening policy (per Morgan), a section on game theory would be most welcome in my opinion, especially as it shows that, if both the player and the host take the game seriously and competitively, the chances of winning by switching are back to 2/3 again. This puts Morgan's 1-q twaddle back in its proper place. Martin Hogbin (talk) 22:24, 18 January 2010 (UTC)

In some ways the Morgan paper can be seen as a dismally failed attempt to discuss game theory. Martin Hogbin (talk) 22:26, 18 January 2010 (UTC)

A question for the 'conditionalists'.

The MHP is notoriously difficult for most people to understand and many peope do not accept the solution even when it is clearly explained to them. In the lead we state, 'Even when given a completely unambiguous statement of the Monty Hall problem, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief'.

Does anyone here think that the above statement does not apply to the unconditionally stated problem, such as that given by Morgan, You will be offered the choice of three doors, and after you chose the host will open a different door, revealing a goat. What is the probability that you win if your strategy is to switch. ?

In other words, does anyone here think that the unconditional problem is not the MHP because it is too easy? Martin Hogbin (talk) 11:00, 17 January 2010 (UTC)

Nijdam, would you care to comment? You say above, 'once the problem is well stated, the soluton is (must be) obvious'. Martin Hogbin (talk) 15:54, 17 January 2010 (UTC)

What is there to be commented?Nijdam (talk) 16:59, 17 January 2010 (UTC)

I take it that you do believe that the solution to the unconditional problem is obvious. Is that right? Martin Hogbin (talk) 20:18, 17 January 2010 (UTC)

Martin - this is the "no-door" version discussed by Krauss and Wang. They consider it an easier version of the MHP, but not the "standard" version. Perhaps it should be discussed in the "Variants" or "Aids to understanding" section. -- Rick Block (talk) 18:03, 17 January 2010 (UTC)

Rick, I understand what the problem is and there is no ulterior motive behind my question. I am just trying to understand your POV. Do you think that the solution to the unconditional problem is obvious? Martin Hogbin (talk) 20:18, 17 January 2010 (UTC)

Why do you care what I think? For editing purposes we actually have a highly reliable source (in fact, a psychology source) that discusses this very question. They say it's an easier version. They say it's not the standard version. My (irrelevant) opinion is that they're right although I doubt that it is a significantly easier version. IMO (more irrelevance) most people would still try to solve this version by thinking about a specific example case - e.g. hmmm, let's say I pick Door 1 and the host opens Door 3, then there would only be two doors left but I still wouldn't know where the car is, so after the host opens a door there's one car and two doors and the chances must be 50/50. -- Rick Block (talk) 20:38, 17 January 2010 (UTC)

I care what you think because I want to resolve this dispute. I am trying to find out why a bunch of, I guess, reasonably intelligent people cannot agree. Both sides seem to keep saying the same thing over and over again but making no impression on the other side. What are we missing? Why do we continue to talk past one another? That is what I am trying to find out.

Nijdam, it would seem, does think that a solution to the well-defined unconditional problem statement is obvious. I have continued this point on the arguments page as I think this may be an important cause of disagreement. Martin Hogbin (talk) 20:56, 17 January 2010 (UTC)

Richard Gill also thinks that the solution to the well-defined unconditional problem is obvious. If the door you first chose has the car behind it with probability 1/3, then switching gives you the car with the complementary probability 2/3, since switchers get the car whenever stayers don't get the car, and vice-versa. He is furthermore really pleased with Boris Tsirelson's proposal to solve the conditional problem under the supplementary condition of *symmetry*, by using *symmetry*. Thus: if after you have chosen door 1 the probability the car is behind each other door is the same, therefore 1/3, and if the quizmaster opens a door by tossing a fair coin when he has a choice, then doors 2 and 3 are exchangeable. Therefore Prob(car is behind 2|player chose 1, quizmaster opened 3)=Prob(car is behind 3|player chose 1, quizmaster opened 2) and both are equal to the unconditional probability Prob(car is behind the remaining closed door|player chose 1, quizmaster opened a door)=2/3. All of this verbal maths argument can be converted into formulas, as I did yesterday. Gill110951 (talk) 21:16, 17 January 2010 (UTC)

When you say obvious, do you mean that most people would be able to spot this solution? 86.132.191.65 (talk) 22:50, 17 January 2010 (UTC)

Yes, spot the solution, or at the very least, quickly understand and accept it when it is presented to them. Martin Hogbin (talk) 11:16, 18 January 2010 (UTC)

Lots of people *do* spot the solution to the unconditional problem. And certainly most people accept it once they have heard it. The exception being lawyers, as was discovered by a survey at the University of Nijmegen. Everyone initially gives the wrong answer (including lawyers), afterwards everyone agrees with the right answer (except lawyers). Gill110951 (talk) 17:28, 18 January 2010 (UTC)

Do you have any more information on what proportion spot the solution without help, and are these results published anywhere. Martin Hogbin (talk) 00:36, 19 January 2010 (UTC)

Explicit assumptions

The 'probabilistic solution' in the article states that "This analysis depends on the constraint in the explicit problem statement that the host chooses randomly which door to open after the player has initially selected the car." Why not mention the other assumptions implicitly made?

This section starts with "Morgan state that many popular solutions are incomplete, because they do not explicitly address their interpretation of the question". And it ends with a solution which does the same. It doesn't make sense. Heptalogos (talk) 12:15, 17 January 2010 (UTC)

This is probably the result of arguments being played out on the page. The best way to correct the problem depends on who you are. I would like to change the first quote to, "Conditional analysis of the problem is only required if it is known that the host may not choose randomly which door to open after the player has initially selected the car." Others may not agree. Martin Hogbin (talk) 12:59, 17 January 2010 (UTC)

Yes (others may not agree). IMO, the article is at this point kind of a mess directly as a result of the senseless bickering on this page. Rather than actually improve the article by presenting a peacefully coexisting (per Boris) pair of unconditional and conditional solutions to the fully symmetric problem, these are being presented (and discussed here) as incompatible solutions. For the symmetric problem these solutions are essentially two sides of the same coin. The unconditional solution says the average probability of winning by switching is 2/3. The conditional solution says the conditional probability of winning by switching in any example case is also 2/3 (which of course means the average must also be 2/3). There is NO conflict between these approaches. You may not think the conditional approach is necessary, but it is certainly not wrong. You may not think the unconditional approach exactly answers the question, but it certainly says what the average probability is. These are both useful solutions, and it is also useful to understand the difference. And, unsurprisingly, this is exactly how most sources (at least most academic sources) treat the problem. -- Rick Block (talk) 18:30, 17 January 2010 (UTC)

I see you both react from your political programs. But I am not at all trying to continue the same discussion from yet another angle. Within the conditional section, which is a valid one as we all agree, I noticed some defects. How can we repair? Heptalogos (talk) 19:35, 17 January 2010 (UTC)

Mo comment was not intended to be political or to be supporting my view. I was just pointing out that, unless we can reach agreement on how to structure the article there is unlikely to be a solution to the problem that you have found. Maybe mediation will help. Martin Hogbin (talk) 20:15, 17 January 2010 (UTC)

An actual suggestion for an improvement rather than continued bickering? WHAT ARE YOU THINKING?  :)

I'd suggest revising the section to be more or less like the relevant paragraph out of the proposed unified solution section, above, which at least is intended to present the conditional approach as an alternative solution without introducing the POV that the unconditional solution is wrong. I think others may disagree that it accomplishes this goal, but I think it's an improvement over what's there now and by working on it together we can make incremental changes toward this goal. -- Rick Block (talk) 20:23, 17 January 2010 (UTC)

As a temporary solution, until we can reach a consensus on how to move forward, I am not fussed. Martin Hogbin (talk) 20:38, 17 January 2010 (UTC)

I like a lot of what Rick Block says above. I would like to underline that there is now a fantastic opportunity to simplify the whole article by presenting the answer to the conditional problem (with the supplementary assumption of symmetry between remaining two doors given player's first choice) as a corollary to the answer of the unconditional problem (with the assumption only that the first choice has probability 1/3 of being correct). My POV is furthermore that since both conditional and unconditional problems are interesting in their own rights and frequently discussed in the literature, both by "amateurs" and by "professionals", both problems need to be treated on the encyclopaedia page. Finally I want to repeat again that Marilyn vos Savant's simply asked "would you switch", she didn't ask for a probability, let alone specifying a conditional or unconditional probability. Personally I think that her problem is a sensible problem and as far as it looks like a math problem, it looks to me more like a problem of game theory than a problem of probability theory, since what the player ought to do depends on what the player believes the quizmaster is doing. Perhaps a sensible player prefers not to follow the advice of a calculation based on a specific assumption about the behaviour of the quizmaster. Perhaps the player would be happy just to discover that by starting with a uniform random choice of door and thereafter always switching (s)he gets the car 2/3 of the time, whatever the quizmaster does, and that this is the best one can hope for. It's amusing that the quizmaster's minimax strategy is actually the symmetric stategy, which makes the conditional probabilities equal to the unconditional ones. Gill110951 (talk) 21:35, 17 January 2010 (UTC)

If only it were that simple. There's still the issue of Morgan saying 'All simple solutions are false', then 'proving' it by contriving a host bias, which leads to the conditional non-symmetrical non-solution which is clamoring for equal time as well. Glkanter (talk) 21:46, 17 January 2010 (UTC)

Now also Gill is presenting his game theory in this section. We should really bring more structure in our discussions. Let's separate possible article restructuring (?) from improving the current structure, which will also be very helpfull in case of restructuring. If you state there cannot be such improvement without agreement on restructuring, then you're actually saying that you don't want to participate, which is really not necessary to mention. So I understand Rick is working out a proposal, which is quite welcome to me. Heptalogos (talk) 22:44, 17 January 2010 (UTC)

I'm not sure what proposal you're talking about. I suggested a unified solution section above. I thought progress was being made, but it was definitely derailed and is somewhat moribund at this point. I think what's actually going to happen is the mediation committee will decide fairly soon whether to accept the mediation request. Although I think it makes sense to wait on structural changes until after we know their decision, there's certainly no harm in making improvements we can all live with in the interim. -- Rick Block (talk) 04:17, 18 January 2010 (UTC)

No structural changes indeed, but (y)our suggestion to revise the section. I don't think that 'the unconditionalists' would mind too much about changes in the conditional section anyway. There are obvious defects that may be repaired relatively easy. Heptalogos (talk) 08:23, 18 January 2010 (UTC)

I now see that you already did change, thanks for that. Heptalogos (talk) 08:47, 18 January 2010 (UTC)

"Suppose you're on a game show..."

"You're" is a contraction for "you are." This means YOU. The reader. Do you know of any host bias? Can you assign anything but a uniform distribution to the host's 2 goat door choice? Glkanter (talk) 18:26, 17 January 2010 (UTC)

If you're not talking about what sources say, this thread belongs on the /Arguments page. Please move it there (or simply delete it since we've talked about this ad nauseam already). Thank you. -- Rick Block (talk) 18:40, 17 January 2010 (UTC)

No, Rick, the arguments page is for this:

"Please place discussions on the underlying mathematical issues on the Arguments page."

I'm not discussing the underlying mathematical issues. I'm discussing how much weight Morgan's paper should receive in the article. That's an article editor's responsibility. Which is the purpose of this talk page.

And we have NOT discussed this before. We have discussed that the MHP needs to be solved from the contestant's SoK. We have certainly not discussed that I, or you, or anyone, as the contestant, have no knowledge of any host bias. Glkanter (talk) 18:55, 17 January 2010 (UTC)

That's really nonsense Glkanter. You are not at all correctly weighing any viewpoint by personally judging the content of a source. Then you found a gap in the reference to the arguments page, misusing that. So we should change the reference from an including to an excluding one: "please post any underlying discussion not directly adressing changes in the article to the arguments page." I suggest that these new sections, including the one from Gill110951, all get removed directly by the admin. Heptalogos (talk) 19:52, 17 January 2010 (UTC)

Hepatlogos: you want to move the new section I wrote to the arguments page. Fine by me, but I put it here because it leads to proposals of how the article could be organised: it can be much shorter and needs much less maths, now we have a short integrated solution to the two main variants which people like to formulate. Gill110951 (talk) 21:45, 17 January 2010 (UTC)

Your arguments cannot lead to acceptable proposals because they are fully POV if there's no reliable source telling us what the MHP is(, but you). Heptalogos (talk) 21:55, 17 January 2010 (UTC)

Glkanter, you are saying that if the player doesn't know anything about the host behaviour, then the player *has* to assign a uniform distribution. I disagree on this. I think that the player has to take account of all possible host behaviours. Gill110951 (talk) 21:45, 17 January 2010 (UTC)

I didn't see this argument coming. Other than, 'Here I am on this game show, heck, I don't know where they put the car', what else is there for me to account for? Glkanter (talk) 21:52, 17 January 2010 (UTC)

Though Laplace promoted it, the argument that ignorance should be represented with uniform probabilities is not much believed these days. Especially when it is not difficult to account for the fact that you don't know the strategy of the quiz-team and quizmaster. It's called game theory. More or less invented by von Neuman, one of the greatest scientists of the 20th century. Nowadays *everyone" knows about it, and it is used and abused all over science and economics and politics. I know of a lot of disasters in applications of statistics where people plugged in uniform probabilities when they didn't know what to plug in, not realizing that this choice can actually produce a very biased/unrealistic answer. EG the legal case of the suspected Dutch serial killer nurse, Lucia de Berk. Gill110951 (talk) 18:23, 18 January 2010 (UTC)

I'm not so good with 'subtle'. And you're raising an issue, 'can we assume a uniform distribution?' that I thought had long been settled. So, if you will, please offer your comments of the Huckleberry section. Glkanter (talk) 18:40, 18 January 2010 (UTC)

Despite the very long discussion we have had, so far all have managed to remain civil, which is to our credit. Demands to move discussions and threats to call admins do nothing to cool tempers here. The only way to move forward is to all try to understand the other side's point of view. That may require still more discussion. That may be tiresome for those that believe the article is right as it is but better to discuss that edit war. I suggested earlier that we all made the effort to use the two discussion pages effectively but said that should be done gently. As the original point was essentially about an underlying philosophical issue I would ask the original poster to consider moving this to the discussions page. Martin Hogbin (talk) 20:35, 17 January 2010 (UTC)

I don't agree that we should account tempers and practice gentleness, or whatever emotions that give the discussion other dimensions than plain reasoning. We'd better also not explicitly imagine such emotions. Heptalogos (talk) 22:15, 17 January 2010 (UTC)

We should always be civil here and it seemed to me that the above conversation was heading in a direction where it could have become uncivil. Martin Hogbin (talk) 11:14, 18 January 2010 (UTC)

Revised version of probabilistic solution

I've edited the content of the Probabilistic section, attempting to make it more NPOV (similar to the proposal above). If anyone violently objects to this feel free to revert, although I hope it is viewed as an improvement. -- Rick Block (talk) 05:41, 18 January 2010 (UTC)

Good change. This is also better explaining how the conditional approach adresses the very specific, although it might not seem to matter in this case. Heptalogos (talk) 08:52, 18 January 2010 (UTC)

Nijdam has reverted this change saying "it was no improvement". More specific comments would be helpful. Another idea is to incrementally edit, rather than revert wholesale. Here's what I changed it to. It was intended to address at least most of JeffJor's comments as well, on the version now archived at /Archive_13#Proposed unified solution section. -- Rick Block (talk) 03:16, 19 January 2010 (UTC)

---

Tree showing the probability of every possible outcome if the player initially picks Door 1

Another way to analyze the problem is to determine the conditional probability in a specific case such as that of a player who has picked Door 1 and has then seen the host open Door 3, as opposed to the approach above which addresses the average probability across all possible combinations of initial player choice and door the host opens (Morgan et al. 1991). This difference can also be expressed as whether the player must decide to switch before the host opens a door or is allowed to decide after seeing which door the host opens (Gillman 1992).

The probabilities in all cases where the player has initially picked Door 1 can be determined by referring to the figure below (note the case where the car is behind Door 1 is the middle column) or to an equivalent decision tree as shown to the right (Chun 1991; Grinstead and Snell 2006:137-138 presents an expanded tree showing all initial player picks). Given the player has picked Door 1, the player has a 1/3 chance of having selected the car. Referring to either the figure or the tree, if the host then opens Door 3, switching wins with probability 1/3 if the car is behind Door 2 but loses only with probability 1/6 if the car is behind Door 1. The sum of these probabilities is 1/2, meaning the host opens Door 3 only 1/2 of the time. The conditional probability of winning by switching for players who pick Door 1 and see the host open Door 3 is computed by dividing the total probability (1/3) by the probability of the case of interest (host opens Door 3), therefore this probability is (1/3)/(1/2)=2/3. Although this is the same as the average probability of winning by switching for the unambiguous problem statement as presented above, in some variations of the problem the conditional probability may differ from the overall probability and either or both may not be able to be determined (Gill 2009b), see Variants below.

Car hidden behind Door 3	Car hidden behind Door 1		Car hidden behind Door 2
Player initially picks Door 1
Host must open Door 2	Host randomly opens either goat door		Host must open Door 3
Probability 1/3	Probability 1/6	Probability 1/6	Probability 1/3
Switching wins	Switching loses	Switching loses	Switching wins
If the host has opened Door 2, switching wins twice as often as staying		If the host has opened Door 3, switching wins twice as often as staying

---

The MHP - relations between sources

Selvin described a problem which he called the MHP. Savant Vos described another problem. Several sources reacted to Savant Vos (Morgan, Gillman, Grinstead) but did not mention Selvin. Who connected Selvin to Vos Savant? Or even more interesting (at least to me): can we create a graphical presentation of the links between all sources?

The reason why this could be interesting to all, is IMO that the question "what is the MHP" can only be answered by such a graphic. Where is the centre of gravity and how are sources connected? If any sources are outside (not connected), they should not me mentioded as the MHP. Heptalogos (talk) 12:46, 18 January 2010 (UTC)

Similar problems.

Can we judge other problems to be similar, if not related by sources? Heptalogos (talk) 12:08, 18 January 2010 (UTC)

Prominence.

I don't think 'weighing sources' is a formal Wiki-term. Only viewpoints in proportion to the prominence of each in the sources is mentioned. What is prominence? Apart from the position of a viewpoint within a source, how about the amount of sources in which a viewpoint exists? How about the amount of readers of a source (and thus the viewpoint)?

If many secondary sources write about a primary source, should the viewpoints of all secondary sources together be more prominent in the article than the viewpoints of the primary source? Would that be strange? Heptalogos (talk) 12:37, 18 January 2010 (UTC)

Any 'source' which attributes to the contestant some knowledge of how the host opens doors is not describing a story problem which begins, 'Suppose you're on a game show...' Which, as I understand it, is how most (all?) popular versions of the MHP begin. Glkanter (talk) 14:24, 18 January 2010 (UTC)

That's your opinion, and you're welcome to it. But since there are not just one or two, but many sources that don't agree with you we have to go with what the sources say. We can't exclude them because of something you or anyone else thinks about them. If it helps you understand their viewpoint any better, just imagine (for yourself) they're saying "Suppose you're on a game show and you knew ...". Furthermore, we can't even say (in the article) anything like "these sources violate the premise that you're on a game show" unless there's some published source we can attribute this to. The bottom line is what you or anyone else thinks about what reliable sources have to say is irrelevant. If they've made egregious errors, there would presumably be other reliable sources that call them on it. -- Rick Block (talk) 15:13, 18 January 2010 (UTC)

No Rick, my paragraph above is not an opinion. It is a logical conclusion. Glkanter (talk) 15:43, 18 January 2010 (UTC)

Rick, you wrote this, above:

"just imagine (for yourself) they're saying "Suppose you're on a game show and you knew ...". "

That contradicts the very essence of a game show. And the problem begins, "Suppose you're on a game show..."

And it's not in an any problem statement. That the host will always reveal a goat, and always offer the switch, have over time become 'accepted' premises. The contestant either colluding or mind reading with the host has not. Glkanter (talk) 16:04, 18 January 2010 (UTC)

@Heptalogos: the notion of prominence (it is also called weight) is primarily discussed in non-scientific articles, e.g. biographies. One example - during the recent US presidential election there was a continuous debate at talk:Barack Obama over how much prominence (if any) to give to Obama's relationships with William Ayers and Tony Rezko. These were stories that Fox News was broadcasting constantly, but mostly ignored by the mainstream media. The point is that accurately reflecting the prominence of a viewpoint within the complete set of reliable sources is an integral part of being NPOV. The readership of a viewpoint is not the issue, but rather the prominence of a viewpoint within reliable sources. One of the goals of this policy is to prevent Wikipedia from being used to promote "fringe" theories or partisan causes (this is policy as well, see WP:NOT#Wikipedia is not a soapbox or means of promotion). Prominence within secondary sources, not primary sources, is exactly what is meant. -- Rick Block (talk) 15:13, 18 January 2010 (UTC)

I have to wonder how prominent a source should be when it is accompanied by a commentary such as Seymann's. Is that common in peer-reviewed professional journals? Glkanter (talk) 15:43, 18 January 2010 (UTC)

@Glkanter, The American Statistician is a peer-reviewed journal for professional statisticians and professional teachers of statistics but not what within professional statistics would be called a research journal. It contains discussion and gossip and a teacher's corner and the like... I am not being disparaging, I am just trying to say that from a professional research-oriented statistician's point of view the journal does not carry a lot of weight and that particular article certainly doesn't contain much work. People who do important novel work publish it in big journals and maybe later do some advertising in The American Statistician. The Morgan et al paper exists and makes an important point which people like to refer to (distinguish conditional from unconditional) so it became a standard reference. At some point no-one reads the references anymore, people just refer to the standard references. The folklore as to "what is" the Monty Hall problem evolves. Science is a cultural, a social phenomenon, as much as anything else. I did not know about te Seymann commentary till I read about it here. He expresses my own gut feelings, I'm glad that that has been written down before. Long live Wikipedia, long live amateur science! You guys are doing the work which the so-called "professionals" (like me) don't have time to do anymore, since we need to spend all our time writing grant applications and grant reports and going to department meetings and doing politics just in order to survive. Gill110951 (talk) 18:16, 18 January 2010 (UTC)

My understanding is that Selvin first brought up the conditional formula a few months after his original letter to the journal. Other than contriving the 'host bias', but not a 'car placer bias', thereby creating an entirely new and different puzzle which is not about a game show, what did Morgan contribute? Glkanter (talk) 18:45, 18 January 2010 (UTC)

The MHP in economics and game theory

Here is what some say is the first solution of Monty Hall by Game Theory:

Barry Nalebuff (1987) Puzzles: Choose a Curtain, Duel-ity, Two Point Conversions, and More. Economic Perspectives vol. 1 nr. 1 pp. 157--163

http://www.jstor.org/pss/1942987

"Puzzle 1" is our very own Monty Hall. I'll try to collect more literature references (and find out what the contents are). But if doesn't belong on the talk page but somewhere else, please move it. Gill110951 (talk) 20:00, 18 January 2010 (UTC)

This is the same Nalebuff reference that's in the article (referred to in the History section). If you want more literature references you might look up the Barbeau references that are in the article. Many of the folks commenting here don't seem to realize this, but it really is quite a good article. Wikipedia's featured article standards are quite high - at least aspirationally equivalent to Brittanica. The sources are generally the original sources for the points that are made, and are the sources that other sources refer to. For example, if you read Rosenhouse's recent book you'll find its references look mighty similar to the references in the article. -- Rick Block (talk) 21:07, 18 January 2010 (UTC)

Rick, what about the issue described above on linking sources? Shouldn't all sources be linked to be addressing the same thing? Would such a presentation be able to show some prominence? Please react above, if you wish. Heptalogos (talk) 21:20, 18 January 2010 (UTC)

The History section of the article contains most of what I have been able to find about, well, the history of the problem. Barbeau's survey (the 1993 one in particular) is quite detailed, but contains nothing in the gap between Selvin's publication in 1975 and Nalebuff's paper in 1987 (which Barbeau does not mention). I haven't been able to find anything that was published in this interval although Nalebuff says "This puzzle is one of those famous probability problems, in which, even after hearing the answer, many people still do not believe it is true" - clearly implying it was famous (at least within academia) by that point. Nalebuff doesn't say where he got it from. There was a mention of it in Mathematical Notes from Washington State University newsletter shortly before vos Savant's first column (I don't have this source). I don't know where Whitaker heard of it. It would be interesting to compare Whitaker's version to the one in Mathematical Notes from WSU. Following the publication in Parade the problem was extremely widely known, both in popular sources and academia. Others on this page have claimed it was an example problem in probability classes at MIT - this is informally supported by a scene in 21, the movie about the MIT Blackjack Team - although I don't know how to pin down exact dates for this. -- Rick Block (talk) 02:38, 19 January 2010 (UTC)

"The basis to my solution is that Monty Hall knows which box contains the keys and when he can open either of two boxes without exposing the keys, he chooses between them at random." - Steve Selvin

The American Statistician, August 1975, Vol. 29, No. 3

http://montyhallproblem.com/as.html

Glkanter (talk) 22:47, 18 January 2010 (UTC)

And vos Savant completely overlooked the "when he can open either" part of this. Do you have a point you're trying to make? -- Rick Block (talk) 01:38, 19 January 2010 (UTC)

Here's more from the same letter:

"Monty Hall wrote..."Oh and incedentally, after one [box] is seen to be empty, his chances are no longer 50/50 but remain what they were in the first place, one out of three. It just seems to the contestant that one box having been eliminated, he stands a better chance. Not so." I could not have said it better myself." - Steve Selvin

So Monty doesn't mention door numbers at all, talks about 50/50, (the probabilities) remain what they were, and 1/3. Steve Selvin says "I could not have said it better myself."

But Morgan and Rick know what the paradox 'really' is, and they claim this isn't it. 16 years and 35 years after Selvin himself already told us it is.

So, let's talk about how much weight to give to various sources. And I don't mean sources in the 'publication' sense. I mean 'sources' as in which author is (most) reliable.

Did the paradox change due to Morgan's paper? For Rick's interpretation to be right, it must have. It didn't. I covered this topic in more detail here. Glkanter (talk) 02:59, 19 January 2010 (UTC)

Are you suggesting some change to the article? If so, please say what it is. Thank you. -- Rick Block (talk) 03:20, 19 January 2010 (UTC)

Well, my contribution to the discussion would be along the lines of, "Selvin directly contradicts Morgan's contrivance of a 'host bias', and also directly contradicts Rick Block's interpretation of what the MHP paradox is. In this light, along with all the other errors and fallacies in the Morgan paper, and presumably those that rely on it, I recommend that Morgan's emphasis in the article be reduced to no more than a footnote in an appendix. Near the end of the article." But that's just my opinion, based on the reliable sources. What would you suggest, Rick? Glkanter (talk) 04:20, 19 January 2010 (UTC)

I would suggest that Morgan et al. is unarguably a WP:reliable source and that since its viewpoint (that the MHP is fundamentally a conditional probability problem) is consistent with a large number of other reliable sources and is a standard (if not the dominant) academic viewpoint, that this viewpoint should be prominently mentioned in the article. -- Rick Block (talk) 05:20, 19 January 2010 (UTC)