Talk:Monty Hall problem

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Former featured article Monty Hall problem is a former featured article. Please see the links under Article milestones below for its original nomination page (for older articles, check the nomination archive) and why it was removed.
Main Page trophy This article appeared on Wikipedia's Main Page as Today's featured article on July 23, 2005.
          This article is of interest to the following WikiProjects:
WikiProject Statistics (Rated B-class, Top-importance)
WikiProject icon

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

B-Class article B  This article has been rated as B-Class on the quality scale.
 Top  This article has been rated as Top-importance on the importance scale.
 
WikiProject Mathematics (Rated B-class, Mid-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
B Class
Mid Importance
 Field: Probability and statistics
One of the 500 most frequently viewed mathematics articles.
A selected article on the Mathematics Portal.
WikiProject Game theory (Rated B-class, Mid-importance)
WikiProject icon This article is part of WikiProject Game theory, an attempt to improve, grow, and standardize Wikipedia's articles related to Game theory. We need your help!
Join in | Fix a red link | Add content | Weigh in
B-Class article B  This article has been rated as B-Class on the quality scale.
 Mid  This article has been rated as Mid-importance on the importance scale.
 
WikiProject Television Game Shows (Rated B-class, Low-importance)
WikiProject icon This article is within the scope of WikiProject Television Game Shows, a collaborative effort to improve the coverage of game shows on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
B-Class article B  This article has been rated as B-Class on the project's quality scale.
 Low  This article has been rated as Low-importance on the project's importance scale.
 

Source for 'Deriving the "standard assumptions"' ?[edit]

The current article contains the parenthetical statement "(From the point of view of subjective probability, the standard assumptions can be derived from the problem statement: they follow from our total lack of information about how the car is hidden, how the player initially chooses a door, and how the host chooses a door to open if there's a choice.)" Can someone provide a source for this claim?IVLeeg (talk) 18:40, 23 June 2014 (UTC)

I am not sure "derive" is the right word for this. These are the Bayesian uninformative priors using the principle of indifference toward alternatives when no difference between them is known. Gill, Richard (February 2011) describes this at pp. 13–14 ~ Ningauble (talk) 20:25, 23 June 2014 (UTC)
"Derive" is definitely not the right word for this. One can't derive assumptions. Also, note that Gill 2011 refers only to some of the trivial and inconsequential ambiguities in the problem statement, which we could agree to forgive by glossing over them with the principle of indifference, but he doesn't refer to the primary ambiguity, i.e., Monty's motives and requirement to always open a door after the initial guess. This ambiguity has a huge effect on the answer, and it certainly can't be resolved in the actual situation by appealing to any principle of indifference. Even with the underspecified and ambiguous problem statement, the player is not devoid of knowledge about how likely Monty is to offer a second choice.
Coincidentally, the wiki editor who inserted the claim that we can derive the assumptions from the problem statement was also named Gill. The Gill 2011 document you mentioned doesn't seem to have been published anywhere (has it?). I think it would be best to have an independent and published source. Failing that, we should either delete the claim, or at the very least the article should say "According to Richard Gill, the assumptions can be derived from the problem statement". That way we won't be misleading readers into thinking it's true.IVLeeg (talk) 22:50, 23 June 2014 (UTC)
I think the wording could be improved, but the use of a standard Bayesian uninformative prior could probably qualify as a routine calculation. If this is not agreed there are many sources which discuss this subject in a way in which it would obviously apply to the MHP. Morgan, in their response to H&N, almost make the point. Martin Hogbin (talk) 08:23, 24 June 2014 (UTC)
The main ambiguity in the problem statement is that it doesn't make clear whether the host must always reveal a goat and offer a change of selections, or whether the host has simply decided to do that in this particular instance (perhaps because the host wants the contestant to change his answer for some reason). There's no "routine calculation" or Bayesian uninformative prior that can resolve this fundamental ambiguity in the problem statement. So, lacking a published reference for the claim that the "standard assumptions" can be derived (or even plausibly inferred) from the problem statement, I think that claim should be removed from the article.IVLeeg (talk) 16:02, 24 June 2014 (UTC)
The text does need to make clear what assumptions are being referred to. The standard assumptions about the game rules are just that, standard assumptions. They seem to be the ones made by most people (I think Kraus and Wang and vos Savant confirm this) and most sources. In general they are not very contentious. Martin Hogbin (talk) 18:22, 24 June 2014 (UTC)
I agree that assumptions (standard or otherwise) are assumptions, and I'm also saying that assumptions are not derived. The statement in the article claiming that the assumptions can be derived from the problem statement is obviously false and, more importantly, is unsourced, and hence should be removed. (Someone suggested sourcing it to the contributing editor's own pdf file accessible on the web, but an unpublished pdf file does not meet the Wikipedia requirements for a reliable source.)
Most of the "standard assumptions" are indeed uncontroversial and inconsequential (hardly even deserving of mention), although one of the "standard assumptions" is quite artificial and unrealistic. Claims that "most people make these assumptions" are unfounded, but that's a separate discussion. All I'm saying here is that none of the assumptions can be derived from the ambiguous problem statement, so the unsourced claim to the contrary should be deleted.IVLeeg (talk) 22:15, 24 June 2014 (UTC)
Gill (February 2011) was the first source that came to mind because he devotes a paragraph to explaining the concept. (Other sources mention it, but this in one of the few sources that even attempts to compare treatments of the problem in an even handed way.)

The citation in the article states that it was published in Statistica Neerlandica 65 (1): 58–71. Does anyone have reason to believe that the citation is false? (Or that the online pdf is substantially different from the paper as submitted and published?) Author Richard D. Gill's presence on Wikipedia is has been duly noted at the arbitration case for this article, and he appears to have complied with the reminder given to him therein. ~ Ningauble (talk) 00:51, 25 June 2014 (UTC)

I see the article includes three references to Gill in 2011, denoted as "2011", "2011a", and "2011b", and the first of these evidently appeared in "Statistica Neerlandica". However, I don't find anything in that paper saying that the assumptions can be derived. (The word "derive" appears only once, and not in relation to assumptions.) He does discuss some of the assumptions, but only the trivial and inconsequential ones, and he does not say that even those can be derived from the problem statement. And he doesn't even discuss the only really significant assumption (about the host's required actions and motivations). So I don't think Gill 2011 supports the statement in the article. This brings me back to my point: If no one can produce a published reference for the (patently absurd) claim that the standard assumptions can be derived from the problem statement, then I think the claim should be deleted from the article.IVLeeg (talk) 03:23, 25 June 2014 (UTC)
Hi guys! Well I am not going to edit the page but I hope it's OK I join in the discussion. Of course there is no way one can *rigorously derive* the formulation of an unambiguous mathematical problem (which might or might not have an unambiguous solution) from a short verbal discussion of a quiz show. That's the whole point of my Statistica Neerlandica paper (did you notice its title?). IMHO model building ie building a bridge from real world to mathematics is an art as much as a science. And depending where you stand you may build different bridges. A carpenter everywhere sees nails to be hammered in. A probabilist sees a chance to do some pedagogical conditional probability calculation. A games theorist sees a wonderful illustration of the minimax theorem. I prefer to go to a higher level, a meta-level, and see an opportunity to discuss model building. To show that there is not one unique right answer but many different answer. The different formulations of problems have different assumptions and different conclusions. There are no free lunches. The more you assume in, the more you can get out. The interesting thing (I think) is to lay bare the various options and show the "consumer" a menu of choices. Expensive five star dishes and light three star dishes. They have different prices, right? It's also pretty pointless to derive assumptions by guessing what went on in Marilyn's or someone else's mind. Once the problem is out there in print everyone's mind approaches it in their own unique way. There's no monopoly to how it should be interpreted. One can discuss historically, culturally, how and why and when different interpretations were made. Richard Gill (talk) 11:54, 28 July 2014 (UTC)

Rewriting the paragraph[edit]

I agree with IVLeeg and think the paragraph should be amended to make it clearer. This is the text as it is now:

'Most statements of the problem, notably the one in Parade Magazine, do not match the rules of the actual game show (Krauss and Wang, 2003:9), and do not fully specify the host's behavior or that the car's location is randomly selected (Granberg and Brown, 1995:712). Krauss and Wang (2003:10) conjecture that people make the standard assumptions even if they are not explicitly stated. (From the point of view of subjective probability, the standard assumptions can be derived from the problem statement: they follow from our total lack of information about how the car is hidden, how the player initially chooses a door, and how the host chooses a door to open if there's a choice.)'

The first sentence does not really make sense as it is. There was a game "Let's make a deal" but it never had three doors, two goats and a car, and it never offered the contestant the opportunity to swap doors. I suggest that we move 'do not match the rules of the actual game show (Krauss and Wang, 2003:9)' and make it clear that the assumptions mentioned do not refer to the game rules but the car placement and host door choice.

The paragraph now becomes:

'Most statements of the problem, notably the one in Parade Magazine, do not fully specify the host's behavior or that the car's location is randomly selected (Granberg and Brown, 1995:712). Krauss and Wang (2003:10) conjecture that people make these assumptions even if they are not explicitly stated. (From the point of view of subjective probability, these standard assumptions can be derived from the problem statement: they follow from our total lack of information about how the car is hidden, how the player initially chooses a door, and how the host chooses a door to open if there's a choice.)' Martin Hogbin (talk) 07:58, 25 June 2014 (UTC)

Looking through the article, comments about the game rules and the standard distributional assumptions seem to be in several places. It would be a good idea to clearly separate these issues and deal with them each once only. Martin Hogbin (talk) 08:02, 25 June 2014 (UTC)

There is a section called Origins and Full Assumptions. Would it be worth discussing the assumptions there? What are the "Full Assumptions"?
  1. The car is placed at random.
  2. The contestant has no knowledge of the car's location.
  3. The host IS aware of the car's location.
  4. The host must always open a door.
  5. The host must always reveal a goat.
  6. The host must always offer the chance to switch doors.
  7. The host never opens the contestants chosen door.
  8. When the host has a choice of doors they pick at random.
  9. The contestant desires the car.
Some of these are referred and sourced in that section (3-8), 2 is never in dispute. 1 makes little difference and 9 is pretty obvious. So how best to beef up the full assumptions section? [SPACKlick]
I tend to agree that this is the best place to discuss the assumptions and that we should avoid excessive duplication. Although they overlap, I think we should try to separate the generally-agreed rules of the game (2,3,4,5,6,7,9) from the assumed distributions (1,8). In some interpretations 1 is very important, the car might always be placed behind door 1, for example.[Martin Hogbin (I presume)]
Martin, I don't agree with your proposed revision of that paragraph, because it removes sourced material and leaves in place unsourced material. My complaint about the existing article is that the parenthetical claim that "the standard assumptions can be derived from the problem statement" is unsourced, so I think it should be deleted, whereas you've proposed to leave it in place. In contrast, the phrase that you proposed to delete actually is sourced. So, I suggest the paragraph be revised like this:
'Most statements of the problem, notably the one in Parade Magazine, do not match the rules of the actual game show, and do not fully specify the host's behavior or that the car's location is randomly selected (Granberg and Brown, 1995:712). Krauss and Wang (2003:10) conjecture that most people make a certain specific set of assumptions even if they are not specified in the problem statement.'
Here I'm assuming that the existing statements are sourced more or less accurately, and I've taken the liberty of adjusting the wording slightly to make the paraphrases at least marginally intelligible. If I've thereby misrepresented the sources, please feel free to correct.IVLeeg (talk) 23:26, 25 June 2014 (UTC)
I don't like referring back to the game show in this section as that will just add further confusion to matters. Would we be better off with a shorter.
Most statements of the problem, notably the one in Parade Magazine, do not fully specify the host's behavior or that the car's location is randomly selected (Granberg and Brown, 1995:712). Krauss and Wang (2003:10) conjecture that most people make a certain set of assumptions even if they are not specified in the problem statement.
and then going on to detail those assumptions? I agree with Martin that 2-7 & 9 are the basic assumptions. I also think that 1&8 are pretty standard assumptions as I've only ever seen them varied when the mathematician doing the varying was consciously varying the problem. I also still think this paragraph should be in the "full assumptions" section rather than sources of confusion. SPACKlick (talk) 11:26, 26 June 2014 (UTC)
Edit to add, the second paragraph of the full assumptions section is, content wise, almost identical to this one. Again we are repeating ourselves. SPACKlick (talk) 11:28, 26 June 2014 (UTC)
I agree about removing reference to the game show (Cf. Hall 1975, already cited in the "History" section) because I do not believe this is a significant cause of confusion, and the source in the article does not say that it is. (Rather, the whole point of the cited section entitled "Are There Possible Effects of Incomplete Information?" (pp. 9–10) is to say ambiguous or incomplete rules are not the cause of confusion.)

Regarding the following sentence, "conjecture" is really not the right word. They do not conjecture that it might be so, they argue that it is so. (p. 10: "We argue that...") ~ Ningauble (talk) 12:00, 26 June 2014 (UTC)

Spacklick says we should not mention the fact that the standard problem statement doesn't refer to the rules of the game show "because it will just add further confusion", whereas Ninguable says we should not mention it because he "does not believe this is a significant cause of confusion". Hmmm... Well, Krauss and Wang definitely mention this (they say "Besides not mentioning Monty Hall's strategy, the standard version refers neither to the exact rules of the game show nor to the a priori probability distribution of car and goats"), so I don't think we should selectively omit this (neither because we believe it adds confusion, nor because we believe it does not add confusion!). The article already mentions that Krauss and Wang argue that many people misunderstand the problem even when the important ambiguity is removed from the problem statement, so that's already covered. The only thing that is not well sourced in this paragraph is the obviously false claim that the important assumption (that Monty must reveal a goat) can be derived from the problem statement. So, I repeat that the unsourced claim should be deleted, and the sourced material should be left in place.IVLeeg (talk) 03:31, 27 June 2014 (UTC)
IVLeeg, I think you have missed the two different types of confusion Ningauble and myself are referring to. I was saying including the reference to the show could be a source of confusion to the reader of the article, Ningauble was saying, as the sources say, that the loose relationship the problem has with the show is not a cause of confusion for the reader/hearer of the puzzle. All that being said, has anyone actually disagreed about removing the reference to deriving the assumptions? I thought we were discussing the best way to do that elsewhere on this page.[note: I do think the standard assumptions can be calculated from the lack of information and symmetry so derived isn't wholly wrong, but it's not an argument worth pursuing] SPACKlick (talk) 08:38, 27 June 2014 (UTC)
I recognized that you were saying that mentioning the unspecified show rules could confuse the readers of this article, and Ninguable was saying the unspecified show rules does not confuse the contestant in the puzzle (or the reader of the puzzle), but I contend that those two propositions are inconsistent. And I further contend that what you or Ninguable (or me) think is irrelevant, since the sources do mention the unspecified show rules. In fact, they report that 13% of respondents answer "switch" when they are told that Monty must always reveal a goat after the first selection. So it obviously was a source of confusion for at least 13% of the respondents. Also, your belief that this information (Monty must always reveal a goat) can be calculated or inferred from the lack of information and symmetry is obviously false, and more importantly, not sourced, so I think you should stop pushing that (unless, of course, you can provide a reliable source). Yes, someone has disagreed (implicitly) about removing the reference to "deriving the assumptions". Martin made a counter-proposal after I posted my proposal, and the offending claim was put back. Also, others (including you) have continued to drag your feet by saying "derived isn't wholly wrong", etc. If everyone is in agreement that the unsourced parenthetical statement should be removed, I will go ahead and remove it.IVLeeg (talk) 12:04, 27 June 2014 (UTC)
To your first contention, it is clearly not inconsistent. The majority of readers of this page will not be familiar with the TV show let's make a deal, nor with the specifics of the choices offered on that show. That is my reasoning for believing it is of better form not to mention that extraneous information. As for the unspecified rules confusing the reader of the puzzle, I cannot find a source to show that the 13% is based on any confusion with the rules of the original show, merely that 13% is the proportion who switch when first told the problem with minor variations fromt he original wording (Granberg and Brown 1995). To attribute that 13% to any form of confusion with the original show is to miss the point of the study. I must admit, I was not directly referring to the fact that Monty must always reveal a goat in my above note, but the three examples specified in the paragraph how the car is hidden, how the player initially chooses a door, and how the host chooses a door to open if there's a choice . I think we can clearly see from this we need a stronger section on the standard assumptions, about which there is further discussion on this talk page. But yes, there is no source for deriving the standard assumptions so the claim should be removed until sourced.SPACKlick (talk) 13:01, 27 June 2014 (UTC)
Okay, I will go ahead and remove the unsourced parenthetical statement.
The point of mentioning that the proposed game does not follow the rules of the TV game show is simply to explain that the Parade problem statement is insufficient to actually imply the claimed solution. If, in the TV show, Monty had played a game as described in the Parade problem, and if he had always been required to reveal a goat after the contestant made their initial choice, then Parade could argued that the problem statement was sufficient (if they had referred to the TV show explicitly), because they could argue that readers should have researched the game show to find out the rules (if they weren't already familiar with it). But of course the game intended by Parade bears no real resemblance to the TV game show, nor to any reasonable behavior in any known circumstance, so the reader has no way of knowing, either by researching the old game show or by any other means, that Monty must always reveal a goat. That's why it's worth mentioning that even though the problem statement refers to a game show, it doesn't actually follow any known game show rules. If it did follow a defined rule, it would eliminate the ambiguity in the problem statement.IVLeeg (talk) 02:35, 28 June 2014 (UTC)
Regarding the TV show specifically:  IVLeeg, I endorsed removing it not just because I believe it is not a source of confusion, but because, as I specifically pointed out, the cited source does not say it is a source of confusion. Yes, they mention that the rules are different from the TV show, but only as a strawman when arguing that not knowing the rules is not what causes confusion in the Monty Hall problem.

The article already describes the TV show in the "History" section, citing Monty Hall himself. Anyone familiar with the TV show must realize this is a completely different scenario: on TV you never get to switch doors. This section is about things that cause confusion, and there are no sources that say anyone is confused about this problem by the rules of the TV show. ~ Ningauble (talk) 16:01, 27 June 2014 (UTC)

I completely disagree. Every reliable source acknowledges that the standard problem statement fails to specify (or even imply) that Monty must reveal a goat, and yet the problem has the standard solution only if the reader makes this (quite unnatural and artificial) assumption. When this rule is made explicit in the problem statement, 13% of respondents correctly say "switch". So the lack of this specification affects how some people answer the question, and part of this lack of specification is due to the fact that the intended problem does not follow the rules of the TV game show (or any other known set of rules). When you say that "not knowing the rules is not what causes confusion", I have to smile. Not knowing the rules certainly OUGHT to cause confusion, since the answer is totally dependent on the rules (i.e., whether Monty is required to always reveal a goat, and if not, what his rule is for deciding whether to reveal a goat). It is lamentably true that many "reliable sources" on this subject are brain dead, so there's a limit to how much this article can be improved under Wikipedia editorial policies. I notice that many of the sources in this article are primary sources (including many from clueless psychologists), which have been synthesized into a narrative by a collection of editors, somewhat contrary to the Wikipedia preference for secondary sources.IVLeeg (talk) 02:35, 28 June 2014 (UTC)
Yes, you are completely right. See my comments in the English and in the German Wikipedia. In the German Wikipedia ("Ziegenproblem") the fact of the missing critical rule of the game is emphasized, but there is too much unessential and superfluous stuff. In a separate section Übersicht über die Fachliteratur zu „dem“ Ziegenproblem we can also find there a nice proof of your observation that many "reliable sources" on this subject are brain dead. The Wikipedia editorial policies are very strange in this case where "reputable nonsense" is used against clear arguments. But, as I wrote earlier, there is a Wikipedia rule, too, which allows that we may simply ignore those rules because we are treating here a very simple problem. We only have to source the strange history of the problem in publications. The original problem in Parade, combined with the claim of a 2/3 solution, is an unintended joke. And that almost all publicists have been fallen for this joke is responsible for the widespread opinion that the pure fact that the host opens a not "chosen" door with a goat leads to a 2/3 solution; not being aware that this solution requires that the host is committed to do so. And the often emphasised "simulations" may be the main reason for this error: For the "simulants", which often present the result as a surprise for themselves, apply the critical rule implicitly.
So we have the situation that people, confronted with the original problem, saying that there is no reason to prefer one of the two remaining doors, are right, and those who say that switching has a 2/3 chance are wrong. And the "1/2 fraction" doesn't need to add a rule to the original formulation of the problem; but the "2/3 fraction" should add the critical rule, but they didn't - or later they did it in footnotes, later sections and so on ...
There is a German article from 2009 which treats all this. We also can find there two letters from 1991 written by the author concerning these critical points.
In the environment here it is very difficult and time-consuming even to bring on simple facts. I wish you success!--Albtal (talk) 12:09, 28 June 2014 (UTC)
@IVLeeg:  Please do not keep misrepresenting what other contributors have said here. I did not say that not knowing the rules is not what causes confusion. I said that this is what Krauss and Wang say. I said it to clarify that they emphatically do not say the rules of the TV show cause confusion. Many sources point out deficiencies in common statements of the problem, but there are no sources that say anyone is confused by assuming the rules of the TV show apply to the problem at hand.

I can agree with the proposition that saying "Suppose you're on a game show" in vos Savant's famous version of the problem (which does not mention Let's Make a Deal or Monty Hall by name), though suggestive in some respects, does little to clarify the rules. Pointing this out does not really add anything to the observation that most statements of the problem do not fully specify the host's behavior. Incidentally, the first published version of the problem, (Selvin, February 1975), is much more true to the TV show (and does mention Let's Make a Deal and Monty Hall by name), but is subject to some of the same ambiguities if one is not familiar with how the TV show works. ~ Ningauble (talk) 13:52, 28 June 2014 (UTC)

Ningauble, as I was typing that last message I originally said "When you say that Krauss and Wang say that not knowing the rules is not what causes confusion...", but that sentence seemed awkward, and it occurred to me that you seemed to be endorsing the statement, so I didn't think you would mind my saying you said it. And I wasn't smiling at who made the statement, I was smiling at the statement. If in fact you do not agree with that silly statement, then I apologize for attributing it to you. On the other hand, if you do agree with that silly statement, then I don't apologize. On the third hand, if you decline to state whether you agree with that silly statement or not, then I decline to reveal whether or not I apologize. (I tell you, Wikipedia is the best entertainment value around...)

But seriously, we seem to be talking past each other. You keep saying no one is confused by assuming the rules of the TV show apply to the problem at hand, but what I'm saying is that people are confused precisely because the rules of the TV show do NOT apply to the problem at hand (nor do any other defined set of rules). In your latest message you allow that Vos Savant's mentioning of a "game show" does little to clarify the rules, but then inexplicably you say "Pointing this out does not really add anything to the observation that most statements of the problem do not fully specify the host's behavior". Why on earth do you say that? She tells the reader they are on a "game show", and you agree that the intended problem doesn't follow the rules of any game show, and yet you say pointing this out doesn't add anything to the observation that her statement of the problem leaves the rules unspecified. It doesn't ADD to the observation, it IS the observation.IVLeeg (talk) 15:08, 28 June 2014 (UTC)

What I believe (though the fact I believe it is irrelevant for Wikipedia's purposes) is that the "standard" problem, as fully disambiguated, is very counterintuitive despite its simplicity, and most people get it wrong. I also believe this is much more interesting than trivial observations about not knowing the rules. Furthermore, though I would not have chosen the wording that Krauss and Wang used, I would make a similar statement: ambiguity in the rules does not explain why most people decline to switch – most people decline the offer even if the problem is stated unambiguously at the outset.

But seriously, although it is appropriate to observe that many statements of the problem, notably the one in Parade, do not fully specify the host's behavior, it is not necessary to point out individual parts of the statement that do not do so. The observation is about what is missing, not what is there. "Suppose you are on a game show" does not impart confusing information, it is merely window dressing. Consider that if mentioning the game show in the problem statement is uninformative, which seems to be Krauss and Wang's point, then mentioning it in this section is also not informative.

I think that mentioning the TV show in this context is excess verbiage in what is already an overly verbose and digressive article. Insofar as this objection may be considered a matter of style, it is not a big deal. Insofar as language in the article may be taken to suggest the analogy with the TV show is a misleading source of confusion, rather than merely uninformative, the article is somewhat misleading and should at least be reworded. Being a matter of substance, this is a somewhat bigger deal. ~ Ningauble (talk) 15:36, 30 June 2014 (UTC)

Yes, this is what the propblem is all about. As you say, 'the "standard" problem, as fully disambiguated, is very counterintuitive despite its simplicity, and most people get it wrong'. Martin Hogbin (talk) 02:56, 29 July 2014 (UTC)

Case Study: Average Person's reason for not switching?[edit]

Here's a good sample of one, found on the web, where a somewhat dull-witted person explains his and his wife's reasoning with the Monty Hall Problem:

Since there are only two doors left for consideration, you now have a fifty-fifty chance of guessing the correct door. After analyzing this far, my wife, Anya, who received a B in Technical Mathematics in St. Petersburg University (in Russia, not Florida), added: "Besides, you never know what motivates Monty to reveal a door in the actual game. I would definitely stick with my first choice."

Here we have someone mixing clearly erroneous reasoning ("fifty-fifty chance since there are only two doors remaining") with an observation that clearly shows she doesn't think Monty necessarily must reveal a door, since she is worried about his motivation, and she thinks it's safest to stick with her first choice, rather than letting Monty entice her into switching.

Later in the web page, after the husband learns the "correct" answer, he belittles his wife for her "error" - but of course it's clear that she was NOT assuming that Monty must reveal a door, and she had a perfectly good reason for not assuming this - it doesn't make sense, and isn't how any real game show is played. On this perfectly rational and correct basis, her answer (that we can't infer a clear advantage to switching) is perfectly correct.

Of course, she also had some incorrect reasoning (although that may have been her husband's reasoning), mixing two different problems, but she had taken Math in college, and was probably more sophisticated than the average person. Now, according to Martin Hogbin, everyone reading the Parade problem assumes that Monty must always reveal a goat, but that is obviously not true. This woman is CLEARLY influenced by the idea that Monty doesn't always have to reveal a door. Does anyone doubt that many people who answer "don't switch" are guided by the same kind of mixed and garbled reasoning, combining some lack of math aptitude with some perfectly valid reasoning about the fact that we don't know Monty is required to reveal a goat, and we don't know his motivation?

Anya was clearly right, along with all the others like her. And yet her nitwit husband was bamboozled into believing she was wrong, because he can't even identify the fact that her reasoning (correctly) allowed Monty to have some choice, whereas the official explanation of the allegedly "correct" answer is based on the unwarranted assumption that the host has no choice. This just shows that it's hopelessly naïve to think ordinary people are even capable of distinguishing between the different conditional bases. They reason intuitively and informally, taking all factors into account.IVLeeg (talk) 06:03, 2 July 2014 (UTC)

The non standard rules are not supported by any source and are completely illogical. See my latest two posts on the /Arguments page. Martin Hogbin (talk) 08:54, 2 July 2014 (UTC)

Now It seems that Martin Hogbin and SPACKlick try to find a way to ignore German sources which contradict them. But the web is full of examples where people show that they don't at all assume that the host is committed to open a not chosen door with a goat and to offer a switch. There is a nice example: A woman said: I would switch, for I don't think that the host is spoofing me.

And "decorating" the MvS problem with formulations which go "just in the other direction" does not only happen in the German speaking area.

And why does Devlin guess a shock for those people who accepted the 2/3 solution, when they later have to take into account that the solution is 1/2 when the host opens a door randomly with the possibility to open the door with the car? - If they had based the 2/3 solution on the crucial rule, they would hardly be "shocked" by this fact. (@Martin Hogbin and SPACKlick: Devlin, like Gardner and others, argues here with a counterexample.)

The "paradox" was born by people who claimed the 2/3 solution without assuming this rule. They thought that the simple fact that the host opens another door with a goat leads to this solution. It is worth to read Selvin's letter which seems to be the starting point of this error.--Albtal (talk) 20:52, 2 July 2014 (UTC)

Devlin's "shock" is that if you were convinced by poor reasoning (The two groups interpretation) then you'll be stunned to see it doesn't work. It makes no comment on whether there is an assumption, implicit in the question, that the host opens a door that is not your door and not the car. If, as seems to be being claimed, the general interpretation of the question in the English speaking world (and I am now convinced that there are significant differences across languages which could be interesting to note in a later section if we could find sources for it) is that monty doesn't have to act how he does then surely you would be able to find people whose response to the myriad explanations was "But, you're just assuming the door he opens is always a goat" or "You didn't account for the host opening the car door" or "So it depends on that assumption, but the question doesn't say that" but you never get that response except from people who have already come to understand the question asked before they interpret it hyper literally to defend their instinct. And again, what is the change being proposed to the article with this discussion?SPACKlick (talk) 21:50, 2 July 2014 (UTC)
The paradox (double chance when switching doors) arises because of the extremely biased role of the host to never show the car, and the article did show the essential difference as follows:
Consider a different problem that contradicts the assumptions of the standard paradox: the host, instead of intentionally revealing a goat, reveals one of the remaining two doors at random. If the host opens a door at random and reveals a goat simply by chance, then the odds are reduced from the standard paradox's 2:1 in favour of switching to 1:1 only. The latter odds track the common intuitive wrong answer because half of the potential winning cases are wasted when the host accidentally reveals the car and by that discards such plain winning event. references
This indispensable hint has been deleted by SPACKlick on 09:52, 18 June 2014, and it is necessary to re-insert that evidence. Gerhardvalentin (talk) 22:15, 2 July 2014 (UTC)
That version of the puzzle is referred in the other host behaviours section as monty fail but you may be right that having it earlier in the article as well might help improve the clarity. Any ideas where and how to insert it without reducing the quality of the article? Could go at the end of standard assumptions something like, "These assumptions are key to the 2/3 result it has been shown (Rosenthal) that changing one of them, say 2, leads to the probaility being 1/2" but written better then I can manage at 20 past 1 in the morning. SPACKlick (talk) 23:19, 2 July 2014 (UTC)
Leonard Mlodinow stated concerning the intended veridical paradox that is based on the extremely biased role of the host to never show the car: "The Monty Hall problem is hard to grasp, because unless you think about it carefully, the role of the host goes unappreciated." (Mlodinow 2008)

That extremely biased role of the host should be emphasised very early, at best immediately after the section "Standard assumptions". Gerhardvalentin (talk) 08:11, 3 July 2014 (UTC)

I agree, a short paragraph at the end or beginning of the assumptions section making it clear that when differing assumptions are made the problem is very different. Possibly linking to the "Different host behaviours" section. As a second Draft [Full section changes highlighted]

The behaviour of the host is the key to the 2/3 solution. Ambiguities in Craig Whitaker's quoted description of game play do not explicitly define the protocol of the host. However Marilyn vos Savant's (1990a) solution printed alongside Whitaker's question implies and both Selvin (1975a) and vos Savant (1991a) explicitly define the role of the host as follows.

  • the host must always open a door that was not picked by the contestant (Mueser and Granberg 1999),
  • the host must always open a door to reveal a goat and never the car
  • the host must always offer the chance to switch between the originally chosen door and the remaining closed door

When any of these asumptions is removed the probability can vary as shown in this section below. It is also typically presumed that the car is initially hidden behind a random door and that if the player initially picked the car, then the host's choice of door to open is completely random. (Krauss and Wang, 2003:9) Some authors, independently or inclusively, assume the player's initial choice is completely random as well. Selvin (1975a)

I don't really like my changes but they're a start...SPACKlick (talk)
Splendid, thank you.  I like the awareness of Mlodinow  in spotlighting this "key" that lets the mathematical paradox arise, especially his "conditioning" on the extreme bias of the host's role, in strictly avoiding to ever show the car. A hint to that aspect – the earlier the better – will help to improve the article, helping to grasp the basics. Gerhardvalentin (talk) 14:38, 3 July 2014 (UTC)
I like it too. One quibble is that I would change 'Craig Whitaker's quoted description' to 'the Parade version'. The Parade version was actually written by vos Savant based on an unpublished letter from Whitaker (who played no further role in the problem). She added 'say door 1' for example.
I would also want to add, before 'When any of these assumptions is removed...', something like, 'These are in fact the assumtions that most people make when they first read the problem' citing vos Savant and K&W. Martin Hogbin (talk) 15:17, 3 July 2014 (UTC)
I'd like a phrase like that as well but I struggle to justify it.K&W's relevant section is
  • If the rule were, instead, that the host has to reveal a goat if the contestant first chooses the car-door and should otherwise do nothing, then p(M3 | C2) = 0, which makes the probability of winning by switching 0 (see Equation 2.1).14 Nickerson (1996) writes: “... without information or an assumption about the host’s behavior, the situation is ambiguous, and the question of whether one should switch is indeterminate.” (p. 420). Most experimental psychologists consequently insert the intended rule “Monty has to open another door and reveal a goat” into the standard version to avoid criticism about ambiguity in the wording.15 But this does not seem to help participants: Although Granberg and Brown (1995) stressed this rule, they observed only 13% switch decisions.
Which doesn't exactly say that most people make this assumption, just that this assumption and incorrect versions of it are not the major cause of the systemic failure to get the correct result. I can't find Anything in Any of the Vos Savant references to show this, the closest I found was "And a very small percentage of readers feel convinced that the furor is resulting from people not realizing that the host is opening a losing door on purpose. (But they haven’t read my mail! The great majority of people understand the conditions perfectly.)" although I haven't seen the 2006 article or her book. — Preceding unsigned comment added by SPACKlick (talkcontribs) 12:05, 4 July 2014‎
The host is bound to maintain strict secrecy concerning the actual location of the car[edit]
I added "The host is bound to maintain strict secrecy concerning the actual location of the car (Henze, 1997)". This central requirement for the intended paradox is well sourced, Norbert Henze is professor in probability theory and stochastics. Imo this is the most important typical requirement to the intended paradox, see inconsistent Morgan et al. 1991, e.g.: In case the host opens his strictly avoided door, then his preferred door actually is very likely to hide the car. Gerhardvalentin (talk) 21:34, 4 July 2014 (UTC)
I have reverted this added emphasis. It is redundant with "reveal a goat and never the car" already in the list. ~ Ningauble (talk) 13:16, 5 July 2014 (UTC)
No, this argument is unsourced. You suppose that "reveal a goat and never the car" to be redundant with "the host is bound to maintain strict secrecy concerning the actual location of the car". But there is no redundance at all, it's two quite different things, as Henze targets quite another aspect. He says Marilyn vos Savant had been accused of lack of knowledge in stochastics, but he strictly contradicts that criticism in characterizing the MHP as follows: It's actually quite mundane, and really has nothing to do with conditional probabilities. Henze says so in contrast to other sources, e.g. in contrast to Morgan et al. who said the probability that the car is behind door 2 can actually be p=1. So, Henze's "keeping the location of the car secret" has quite another direction and purpose that is never covered by "always a goat and never the car". Please re-insert that characteristic and distinguishing aspect that is specifically important for depicting the MHP. — Preceding unsigned comment added by Gerhardvalentin (talkcontribs) 15:07, 5 July 2014)
Might not this comment be better somewhere else. As I see it, it is is more criticism of the Morgan approach in that it says that, by his actions, including his choice of door to open, the host cannot reveal any information which would give a clue as to the likely location of the car. I think it is an important point, made by a reliable source, but it is not one that affected most people's thinking on the subject until Morgan raised the spectre of host door choice. Martin Hogbin (talk) 17:18, 5 July 2014 (UTC)
Quite the contrary, I strictly oppose. More than 20'000 pages about "simple puzzle" versus "can only be solved by conditional probability", including ArbCom, is enough. And enough is enough. Henze's "It's actually quite mundane, and really has nothing to do with conditional probabilities" versus thousands of arguments "after the host has opened door #3 to show a goat, the probability that door #2 contains the car can obviously be p=1". Never trivial, Henze raises a very clear light on this eternally ongoing conflict and it is a real coup. His saying "the host has to maintain secrecy concerning the actual location of the car" is not just incidental. After naming the necessary requirements of the paradox, he then expressly adds: "In all these considerations, of course, it is crucial that the host is bound to maintain strict secrecy concerning the actual location of the car", naming the central importance of this condition as the starting point for the arising of the paradox. Henze explicitly denies that conditional probability is "necessary" to solve the puzzle that actually is "quite mundane, and really has nothing to do with conditional probabilities". For solving the paradox, "BEFORE" versus "AFTER", did he open #2 or #3, is addressing the host's choice of two goats in 1/3 if the contestant initially picked the prize. More than 20'000 pages are enough, so this central prerequisite has to be in the article. It's really not about "never shows the car". It's the central prerequisite for the arising of the clean paradox that "has nothing to do with conditional probability" (Henze). Gerhardvalentin (talk) 19:14, 5 July 2014 (UTC)
That was my point. Henze is is pointing out that the Morgan solution is wrong, or at least not necessary. I agree, but how can we demonstrate that the Morgan solution is wrong before we have given the Morgan solution. No one is going to understand what point is being made by Henze.
All that I am suggesting is that we do have the Henze point, as made by you, but later on in the article. Martin Hogbin (talk) 19:46, 5 July 2014 (UTC)
You say "No one is going to understand what point is being made by Henze." It's on a famous "paradox", and it is necessary to name the basics of this paradox, just in the beginning. The crucial point of the matter is the role of the host that generates the paradox, and the most important constitutive basis that does distinguish this famous paradox from quite other variants (of "differing results") is that the host is bound to secrecy regarding the actual location of the car, in any way and whatever that means. It is necessary to name this prerequisite just in the beginning, in first place. It is well sourced and may not be neglected. Later on in the article, you can still refer to this very important main argument. More than: 20'000 pages is enough. Gerhardvalentin (talk) 20:59, 5 July 2014 (UTC)
The point made by Henze is a subtle one and it surely will not be obvious to a first time reader of this article why 'the host must always reveal a goat and never the car' is not the same as, 'The host is bound to maintain strict secrecy concerning the actual location of the car'. We know that Henze is having a swipe at Morgan but who would possibly know that until they have seen Morgan's argument. So, are we agreed that the Henze quote should go after the conditional solutions are explained in the article. Martin Hogbin (talk) 21:59, 5 July 2014 (UTC)
Seems you forgot about ArbCom. You suggest to maintain turbidness. My answer is no, never. Because the world famous intended paradox forever has suffered from ambiguity, and ambiguity forever had been the pitfall of this intended paradox. This is the very reason that, from the start, unambiguous specification is indispensable. The possible question "why must the host ..." is secondary. But – indispensably – absolute clarity must be the foreground. The "why" is secondary, space enough to give the answer "why". See all the deviant variants of cross-purposes that were presented in abundance and abundance. Evidence enough. And btw: Morgan et al. are not wrong, they did address a special variant. Henze does make that clear distinction. Finally, the article owes clarity to the readers, in distinguishing the intended paradox from other variants. In case you don't dare to, then I will have to be going to revert Ningauble's deletion of sourced contents, his deletion having been based on an inapprehensible comment "already in the list". Again, evidence enough. It's on cross-purposes, and it's on distinguishing the clean paradox. No way out. Gerhardvalentin (talk) 00:14, 6 July 2014 (UTC)
I agree that it is important to maintain clarity at the start of the article, so that it is accessible to as wide a range of readers as possible. For that reason we should start with the simple, 'clean' as you call it, paradox, without complicating factors. That is what was agreed at the, very thorough, RfC that followed the ArbCom case. After the simple paradox has been presented we can go on to discuss the various distracting complications that turn a simple puzzle, that (almost) everyone understands perfectly well but still gets wrong, into an endless discussion between mathematicians, statisticians, psychologists, and anyone else who wants to give an opinion.
The fact that the host must keep the location of the car secret is assumed by nearly everyone without much thought. Henze's point is that, if we are to consider the door opened by the host to be important then we must take it that the host is providing information as to the whereabouts of the car, contrary to our initial assumption. Thus Henze's point is a clever argument against an unnecessary complication, the Morgan solution. As such it is itself a complication that can wait until later to be discussed.
More important, in my opinion, is to state that the standard assumptions are the ones that most people do, in fact, make thus closing another loophole for people who get the answer wrong. I have no way of proving this but I would bet that nearly everyone who thinks up a complicating factor, from Morgan onwards, did so in response to having got the answer wrong themselves. Having done so, and having been embarrassed their error, they look for ways to justify their wrong answer; what if the host did not always offer the swap, what if the host had a door preference, what if the host could reveal the car etc. In my view, 'nice try but no cigar'.
So, I agree with you. Let is keep it clean and simple at the start and on that basis the Henze statement is not necessary there, although I agree it is a good argument that should be included in the article somewhere. Martin Hogbin (talk) 10:05, 6 July 2014 (UTC)
Not somewhere, but where it belongs.
Yes, it is necessary to start with outlining of the host's role "the host must always ..." – No redundancy, Henze was not joking in expressively adding the top priority to that outlining of the host's role: "In all these considerations, of course, it is crucial that the host is bound to maintain strict secrecy concerning the actual location of the car". No redundancy at all, Henze knows exactly what he says. This top priority belongs where Henze decided it to belong, it belongs to the outlining of the host's role and its restrictions. I'm going to add this top priority to the outlining of the host's role, verbatim according to Henze's judging, and I hope you agree with his judging. Gerhardvalentin (talk) 12:20, 6 July 2014 (UTC)
I agree with you about the importance of Hentze but am trying to come to some kind of compromise that other editors will accept. If you want to fight it out I will leave you to it. Martin Hogbin (talk) 14:05, 6 July 2014 (UTC)
Have to say, I agree with Gerhardtvalentin, It's an important assumption, mentioned in various forms in several sources, that the Host doesn't reveal and the Contestant doesn't know where the car is. I'm not certain Henze's phrasing is the best for the beginning of the article, because it's phrased that way to account for other details. They key implication of it, in the simple form, is the contestants ignorance not the hosts complicity in that ignorance. SPACKlick (talk) 06:33, 7 July 2014 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────I agree that it should go in the article; it is a very important point. I personally have no objection to its going near the beginning although I am sure that most readers will not understand its real significance. That is one reason that it would be better placed later on. The other reason is that it seems that others do not want it included near the start, if at all, and I am trying to find a compromise. If it turns out that there is actually a consensus to have it where Gerhard put it that is fine with me.

Regarding its meaning, I take it to mean that we should ignore the host's choice of door when the player has originally chosen that car, because there can be no information about where the car is revealed by the hosts choice of door because the host is strictly forbidden from revealing such information in any way. I have not read what Henze says in full because I think it is only available in German. Does anyone have a translation? Martin Hogbin (talk) 08:33, 7 July 2014 (UTC)

Exact. Other sources "seem" to base on the host's complicity in that ignorance, in predicating "if the host has the choice between two goats, then he chooses equiprobable" – but not really meaning that the host really did flip a coin, but that we have to base on "... as if the host did flip a coin". Henze draws attention to that important principle in another way in saying that the actual location of the car remained secret.— Preceding unsigned comment added by Gerhardvalentin (talkcontribs) 08:24, 7 July 2014)
I may have misundestood Henze's point. If this premise is merely a rewording of the equiprobable decision between two goats, then it can go in and should be phrased this way, not in a roundabout fashion to do with secrecy. Whereas if you are sourcing a need to include the assumption that the contestant holds ignorance then it would need to include secrecy. That said, if you are simply trying to include the equiprobable choice assumption it really doesn't need to go in this early. SPACKlick (talk) 10:03, 7 July 2014 (UTC)
the actual location of the car remains secret[edit]

Should it read:

  1. the host must always open a door that was not picked by the contestant (Mueser and Granberg 1999),
  2. the host must always open a door to reveal a goat and never the car
  3. the host must always offer the chance to switch between the originally chosen door and the remaining closed door
  4. In all these considerations, of course, it is crucial that the host is bound to maintain strict secrecy concerning the actual location of the car (Henze 1997)

or it could read:

  1. the host must always open a door that was not picked by the contestant (Mueser and Granberg 1999),
  2. the host must always open a door to reveal a goat and never the car
  3. the host must always offer the chance to switch between the originally chosen door and the remaining closed door
  4. after the host has shown a goat, the actual location of the car did remain strictly secret (Henze 1997 and others)

What is the best way to show this principle? Or should it read   4. if the host, in opening of a door, did have the choice between two goats to show, then it is assumed that he chose one of them with equal probability

Anyway, this standard assumption has top priority for understanding the clean paradox. This standard assumption should be shown where it belongs. Other proposals? Gerhardvalentin (talk) 08:34, 7 July 2014 (UTC)

To make the wording accurate and consistent, closer to your last option is best

  1. If there is a choice between two goats to reveal, the host chooses at random with equal probability.

Does that define the assumption you're looking to add? SPACKlick (talk) 10:06, 7 July 2014 (UTC)

Thank you yes, that is the way and the standard formulation that most sources use to underline that – in that situation – we "are to assume" that there was no host's door preference, and both goats were equally likely to be revealed. Yes, that's exactly the point. But I do not like that many sources say "the host flipped a coin", as this sounds like a procedural instruction to the host, whereas it only signalizes that "we have to take it as given" that the host chose at random. So I suggest the wording
  1. If there is (or was ?) a choice between two goats to reveal, it is assumed that the host chooses (or chose ?) at random with equal probability.
I would appreciate if you could enter it as the most used standard assumption ("it is assumed that" is my addition). But I do like Henze's formulation as well, as it is a more general way to express that fundamental principle of the standard paradox and its surroundings. Gerhardvalentin (talk) 11:15, 7 July 2014 (UTC)
You are aware the article currently says "It is also typically presumed that...if the player initially picked the car, then the host's choice of goat-hiding door to open is completely random."SPACKlick (talk) 08:10, 8 July 2014 (UTC)
I think that it is wrong to single out this particular distributional assumption from the others that are generally made, which are that the car and goats are placed uniformly at random at the start of the game and that the player's original choice is uniform at random. The three assumptions together then lead to an obvious and intuitive symmetry with respect to door identity which means that we can forget door numbers completely.
Henze's comment is more of a general principle,which has further reaching consequences that most people imagine and I therefore think that should go in the article somewhere. I personally would be happy with it here, even though its real significance would not be clear to most readers, but I would also be happy to have it later on when condition probability is mentioned. You will have to argue that one out. By the way, I have asked Ninguable to explain his removal of the Henze comment.Martin Hogbin (talk) 09:11, 8 July 2014 (UTC)
Thank you. Imo the first suggestion above (the actual location of the car remains secret) is best, item #4 is what Henze says:
  1. the host must always open a door that was not picked by the contestant (Mueser and Granberg 1999),
  2. the host must always open a door to reveal a goat and never the car
  3. the host must always offer the chance to switch between the originally chosen door and the remaining closed door
  4. In all these considerations, of course, it is crucial that the host is bound to maintain strict secrecy concerning the actual location of the car (Henze 1997)
It's all about the unequivocal representation of the abstract paradox. Henze, well knowing about crucial misunderstandings and controversial issues, considers this generalization to be absolutely necessary, and for that very reason the article should pay regard to it. Imo this generalisation should be mentioned as item 4.
Hoping Henze's general clarification can and will help to avoid further upcoming doubtings and misunderstandings as to the intendedd abstract paradox. Gerhardvalentin (talk) 10:02, 8 July 2014 (UTC)
I'm sorry but that wording is just unhelpful in the context of the assumptions section. I imagine it reads much better in Henze's paper, although I can't access it or a translation. I also believe that it is right that this assumption is separate from the major three because the major three must be true and known to the contestant in order for the paradox to work. This one must either be true, true and known or false and unknown. The only time it makes a difference is if the distribution of probability of the host choosing between two goat doors is not 1:1 and the contestant knows that. Even then unless the distribution is 1:0 then the decision, switch, is unchanged. SPACKlick (talk) 11:40, 8 July 2014 (UTC)
And even the distribution is 1:0 the decision, switch, is unchanged, because staying never can be better. But Henze makes a clear distinction between exercises in conditional probability, and the clean paradox. You may not see Henz's motive as a professor in probability and stochastics, but he calls it: "Bei allen diesen Betrachtungen ist natürlich entscheidend, dass der Moderator die Autotür geheimhalten muss ..." (crucial, essential). As the paradox does not allow for 1:0 or other variants besides 1:1. And, not least, it's on the clean paradox, also. Not only on exercises in probability theory. Gerhardvalentin (talk) 12:02, 8 July 2014 (UTC)
Sorry, I don't see it as an essential for simple considerations of the paradox or basic understanding of the paradox. It is already referred, as I said above, as a general assumption just not one of the 3 key assumptions. Can you link me to a translation of henze's paper (or the original German and I'll struggle through it). It gets detailed treatment later in the article. Why needs it be here? SPACKlick (talk) 12:08, 8 July 2014 (UTC)
Have only the German edition and can send it if required. Henze is professor in Karlsruhe in probability theory and stochastics, and he knows exactly what it needs to distinguish the intended paradox from variants, and his clarification is important enough. He is also on youtube: (http://www.youtube.com/watch?feature=player_detailpage&v=NcCGgdornVs#t=4150] Gerhardvalentin (talk) 12:48, 8 July 2014 (UTC)
Ok, having read, to the best of my ability [I'm not good at German], the relevant chapter of the paper, the comment reads quite throwaway. My best translation of the section is
  • This argument becomes even more clear when considers the prospects of success of the strategies of a switcher" and a stayer. The stayer wins the jackpot, if the prize is behind the door initially chosen and the probability of this is 1/3. A switcher, however, wins the car when he first chooses one of the two "goat's doors", probability 2/3, because after the opening of the other goat's door by the host, automatically leaves the changing strategy with the car door. In all these considerations, of course, it is crucial that the moderator must keep the car door a secret and is also required to open a goat's door."
It doesn't appear to be about the equiprobable choice (it may go on to that later I haven't translated more than 3 paragraphs of the paper). It seems to be expressly about not opening the car door and being forced to open the car door. SPACKlick (talk) 14:00, 8 July 2014 (UTC)
It looks that way to me too. I have never seen the original so maybe I have misunderstood it. Martin Hogbin (talk) 14:13, 8 July 2014 (UTC)
Sources showing most people make the standard assumptions[edit]

Krauss and Wang have a whole section on this subject entitled 'Are there possible effects of Incomplete Information'. At the end of that section (page 10) they say, 'In sum, when solving the standard version, in which the required assumptions are not made explicit, people seem to assume the intended scenario anyway'. They go on to quote vos Savant (no doubt we can find her original) who said, 'Virtually all of my critics understood the intended scenario...'.

K&W go on to say, 'In short people struggle not with the ambiguity of the standard versions assumptions, but with the mathematical structure of the scenario'.

This is two solid reliable sources who say very clearly that most people did make the standard assumptions. Martin Hogbin (talk) 13:36, 4 July 2014 (UTC)

Can we add this somewhere please. It really is not disputed by reliable sources. Martin Hogbin (talk) 14:14, 8 July 2014 (UTC)
I still disagree that the sources show what they claim. I'm not overly objecting to putting it in because it matches my personal experience but I'd like it to be noted that I think there should be a stronger source for that claim. K&W have
  • "After the Monty Hall problem became famous, many questions on possible effects of incomplete information in the standard version arose. Besides not mentioning Monty Hall’s strategy (1), the standard version refers to neither the exact rules of the game show (2) nor to the a priori probability distribution of car and goats (3) (c.f., Nickerson, 1996; von Randow, 1993; Mueser & Granberg, 1999).
  • ...[A section on each or (1)-(3) including] It can be read in Ichikawa (1989, p. 271) that letting participants know Monty Hall’s strategy does not help them find the solution either...
  • ...Most experimental psychologists consequently insert the intended rule “Monty has to open another door and reveal a goat” into the standard version to avoid criticism about ambiguity in the wording.15 But this does not seem to help participants...
  • ...[followed by]We argue that most of the criticisms of the standard version regarding its unstated assumptions are mathematically relevant, but not psychologically relevant, since the intended assumptions will hold anyway....
  • ...Let us give examples of how assumptions, different from the intended ones, would make this “uniformity belief” in the standard version impossible:...
  • ...[a section on various strategies of Monty that don't result in 1/2...
  • ...In sum, when solving the standard version, in which the required assumptions are not made explicit, people seem to assume the intended scenario anyway. Along the same lines, vos Savant observed...
  • ...In short, people seem to struggle not with the ambiguity of the standard version’s assumptions but with the mathematical structure of the scenario....
  • ...what blocks correct intuitive reasoning is not lack of information, but lack of the right information representation.
What I take from this is "The failure to express the assumptions is not what causes people to make mistakes of reasoning" not "Here it is clearly shown that people make the absolutely correct assumptions about the rules of the game". They make that claim, in passing, but fail to support it. That's why I'm dubious here. SPACKlick (talk) 15:07, 8 July 2014 (UTC)
The MHP is a *joke*, a *trap*. The whole point is that people instinctively give the wrong answer for different intuitive reasons some connected to bad probability reasoning some to unwarranted psychology thinking. And when you tell it to people there is a *dialogue*. So you explain the "real assumptions" if and when needed. Richard Gill (talk) 11:58, 28 July 2014 (UTC)
Maybe we are taliking a little to cross purposes here. By standard assumptions I am talking about the game rules: that the host must always open an unchosen door to reveal a goat and must always offer the swap. As vos Savant said, 'people seem to assume the intended scenario anyway'. That seems pretty clear to me.
What people assume about the host's door opening strategy is another matter. The probably do not think about it at all. Martin Hogbin (talk) 02:49, 29 July 2014 (UTC)
Richard, I do not understand in what sense the word 'joke' applies to the MHP. Martin Hogbin (talk) 03:19, 29 July 2014 (UTC)

Vos Savant and the media furor out of place[edit]

With the recent changes to the article the media furor section seems out of place. The article goes [Lede, Paradox, Assumptions, media furor, Solutions, Confusion and criticism]. I think it may work better if Furor was moved between solutions and Confusion and criticism, particularly in light of "A second controversy" That said, I think a lot of it can be removed. The article is about the puzzle, not necessarily about the parade column. I'm not confident enough in this to WP:BRD it and would rather discuss first. SPACKlick (talk) 15:31, 8 July 2014 (UTC)

It is what changed the problem from being an obscure mathematical puzzle to being famous. It shows just how many people not only get the answer wrong but are ready to berate those who give the correct answer in print. Martin Hogbin (talk) 02:59, 29 July 2014 (UTC)
I fully agree it needs to be there, it's why it's famous. However the way the article reads right now is a little odd and it takes nearly 1500 words to get to actually discussing the problem. SPACKlick (talk) 09:23, 29 July 2014 (UTC)
I don't think the section is misplaced, but I agree that it is overlong: the "little green woman" and the "second controversy" subsections are misplaced here.

A brief treatment of how the Parade column met with utter disbelief, and was picked up in mass media (The New York Times), is appropriate here. The shell game analogy and the little green woman scenario do not belong here, before solutions are presented. (Years ago we had an "aids to understanding" section for this sort of thing.) Material about criticism of solution methods, now shown as "A second controversy", definitely belongs in the section on "Criticism of the simple solutions", after all of the solutions have been presented. ~ Ningauble (talk) 10:14, 30 July 2014 (UTC)

Furor is a little NPOV[edit]

Is there a reason we're using the term "Media Furor?" rather than "Media Response"? Furor suggests anger and rage and over excitement. Response seems more neutral. SPACKlick (talk) 15:40, 8 July 2014 (UTC)

'Anger and rage and over excitement' is a pretty good description of the letters vS got. Martin Hogbin (talk) 03:00, 29 July 2014 (UTC)
Is the term sourced to anywhere though? I'd rather keep within Wiki Standards and use a neutral term like response than a loaded one like Furor SPACKlick (talk) 09:20, 29 July 2014 (UTC)