Wikipedia talk:Arbitration/Requests/Case/Monty Hall problem/Proposed decision

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Finding of fact

One divided by two equals two Two children are fighting over a piece of chalk. An adult intervenes by breaking the chalk in half and handing a piece to each child. One child immediately sees that division results in more pieces of chalk and, delighted by this bounteous doubling, happily begins doodling. The other child sees that division results in having less chalk and, outraged by this meager halving, throws it away in disgust. Whether or not one of the children's perspectives is unreasonable, neither child is mistaken about the math. The relevance of mathematical "truth" depends upon one's understanding of what the problem is about. (Story adapted from a talk by Ray Bradbury circa 1975)

A stated finding of fact is [my bold]

"The Monty Hall problem is unusual in that while there are many scholarly sources, the key source is a popular one, and the best known and most often quoted formulation of the problem and it's solution is 'wrong' in terms of advanced probability theory. This has led to a tension in the article between demonstrating the simple proposition in the popular sources, and providing the 'correct' Bayesian formulations of the advanced probability versions".

I am somewhat surprised that the arbitrators seem to have made a decision on what is a matter of fact regarding probability theory, especially as they refuse to be drawn into making a content decision. Martin Hogbin (talk) 21:45, 13 March 2011 (UTC)

You are probably right about that, it is klutzy phrasing on my part. I will try a rephrase - what I'm trying to explain is why there is a "pov" about a maths problem, given that most people will believe that maths problems only ever have one answer. --Elen of the Roads (talk) 22:35, 13 March 2011 (UTC)

I concur with Martin. It might be more appropriate to express this in terms of that formulation of the problem being open to interpretation. As remarked in the article, "almost all sources make the additional assumptions." It may be noted that scholarly sources find the proffered solution does not satisfy strict readings of the formulation. It might be too much of a stretch to assert that the consensus of scholarly sources finds there is no reasonable interpretation under which the proffered solution is correct. ~ Ningauble (talk) 22:41, 13 March 2011 (UTC)

See if what I have changed it to is any better. I'm not trying to say it what is actually right or wrong, just that there is this viewpoint. Elen of the Roads (talk) 22:46, 13 March 2011 (UTC)

Better, but "should not be included in the article" probably overstates the position of the major faction. It seems more a dispute about how to include it, in terms of viewing it as deficient or not. I may suggest alternative language at the Workshop tomorrow, but I fear I lack the wit to achieve brevity. ~ Ningauble (talk) 23:53, 13 March 2011 (UTC)

The rewording morphed the statement from being about external factors to being about what "some proponents" allegedly want (and, if you mean to be including me in "some proponents" this is NOT what I want). I think keeping this externally focused would be better. I don't know if it's out of line to make a suggestion, but perhaps something like "In the literature, some proponents of a more complex Bayesian solution argue that the simple solution technically addresses a slightly different problem. This has led to a tension in the article between demonstrating the simple proposition in the popular sources, and providing the more complex Bayesian formulations commonly found in scholarly sources." -- Rick Block (talk) 00:14, 14 March 2011 (UTC)

Good point, that's what I get for rewriting on the fly. It's the external sources that I'm trying to get at, not the view of the article editors. I have left it at 'wrong', as that seems a plain english explanation, which is all that I'm after. Elen of the Roads (talk) 00:48, 14 March 2011 (UTC)

Two problems here. (1) A formally posed Maths problem might in general have a unique good solution, and of course many good paths to the good solution, but Vos Savant's words are already semantically ambiguous. To convert them into a formal math problem is a problem of mathematical modeling of the real world:and that is an art, not a science. There is no unique correct *math question* to answer. (2) MHP also found its way into game theory, mathematical economics, decision tbeory, optimization theory. It is not only commonly found in statistics textbooks, where it functions as a fun example for people struggling to learn Bayes theorem, but also commonly found in game theory textbooks, etc, etc. Where the same words of Vos Savant are converted into a different math problem. Richard Gill (talk) 15:57, 14 March 2011 (UTC)

As someone else has said, perhaps the problem is that it's not one problem but many, which appear superficially similar. But in plain English, one bunch of mathematicians disagree with what another bunch is saying. People who never looked at maths past High School would be surprised by that - to them, maths problems only have one answer. Elen of the Roads (talk) 16:23, 14 March 2011 (UTC)

Yes! And: that mathematicians, especially applied mathematicians, often disagree, is why Maths is so great, still alive and flourishing and going new places where it's never been before! Unfortunately many school teachers don't know this, don't want to know this. That's why nowadays children with a real aptitude for Maths usually don't discover they have the talent, so they are lost to business studies or something trendy multidisciplinary where they never learn a discipline of their own: they just learn how to copy and paste from Wikipedia. Richard Gill (talk) 16:56, 14 March 2011 (UTC)

Yes Elen, one bunch of mathematicians disagree with what another bunch is saying. Not to put too fine a point on it, but in the current version,[1] on which voting has begun, isn't it insufficiently neutral to note that "some" sources deem it wrong without also noting that other sources deem it right?

"Complex Bayesian formulations of the advanced probability" may not be the clearest way to indicate for a general audience that this represents an epistemological perspective, and is not simply a matter of being complex or advanced. For the purposes of this finding it might be better to simply note that some sources disagree with 'simple' treatments and with each other, rather than get into particular philosophical interpretations of probability upon which some of the disagreements are based. (Bell (1992): "I will leave it to readers as to whether this equivalence of the conditional and unconditional problems is intuitively obvious.")

The special challenge for editors that this finding represents is not just that there are differences of opinion, but that some of the most important sources are from different worlds of discourse. ~ Ningauble (talk) 18:23, 14 March 2011 (UTC)

WP:TECHNICAL and comments by Geometry guy

I have been watchlisting this case for some time, but have been reluctant to contribute because of the endless talk associated with what should be a straightforward and very interesting Wikipedia article.

I am commenting here primarily because of the reference to WP:TECHNICAL, a page whose status has been disputed recently (not by me), and whose nutshell ("Strive to make each part of every article as accessible as possible to the widest audience of readers who are likely to be interested in that material") is based closely on a comment of mine. There are many nuances connected with this nutshell, and arbitrators may be in danger of implicitly making a resolution on content if they do not take on board the distinctions. Geometry guy 00:34, 14 March 2011 (UTC)

I read the whole guide, not just the nutshell. You'll also note I haven't quoted the nutshell. --Elen of the Roads (talk) 00:36, 14 March 2011 (UTC)

You are one of the most incisive and clear thinking arbitrators Elen: that is why I voted for you, after all!

I have no doubt that you read the whole guide, but please do not rush to respond or conclude: I was providing context for the current form of the guide, which, if you check the talk page and edit history, has been under flux recently. I have more to say, but prefer to encourage editors to read, rather than write, so I will delay further comment. Geometry guy 01:01, 14 March 2011 (UTC)

I see your concern, but the point is not to exclude material because it is too simple. TECHNICAL itself recommends putting the simplest version first, and the more complex material later in the article, so that the person who simply wishes to be better informed can get an insight into the subject, even if they give up as soon as the maths notation, Greek or diagrams appear. --Elen of the Roads (talk) 01:17, 14 March 2011 (UTC)

I'm not sure that my concern was yet clearly enough expressed above for you to "see", but regarding your subsequent comments, I agree with you entirely. Since the current form of WP:TECHNICAL is influenced by my comments, as well as more substantial contributions by editors I greatly respect, such as CBM, my support for the current version is unsurprising.

Beginning an article with simpler approaches, and discussing more technical details later is, in my view, a no-brainer, yet this has been a significant topic of argument, not only at arbitration here, but throughout the history of the article (which I first encountered in 2007). There have been many discussions about technical content across Wikipedia: the talk page history of WP:SCG provides further examples.

I do not envy arbitrators who have to provide findings in such complex circumstances. The concern I have is that conclusions drawn here, which may seem reasonable in this case, may inadvertently result in collateral rulings on content which go beyond ArbCom's remit.

Pause.

The statement that "routine arithmetic is okay" may suggest that other straightforward logical and mathematical deductions are not acceptable without citation. If A is smaller than B and B is smaller than C, is it okay to deduce that A is smaller than C? What if 10 letters are sent (reliably) to a mailing list of only 10 people and no one on the list receives more than one letter. Is it okay to deduce that everyone on the list receives a letter? Is it okay to deduce that the sum of two even numbers is an even number? If x belongs to a set A, but does not belong to a set B, can we deduce that x does not belong to the intersection of A and B? What if a function f(x) is increasing as a function of x, and its value f(0) at 0 is positive: can we conclude its value f(1) at 1 is also positive? These examples may seem trivial, but it is just as trivial to deduce that a group has only one identity element, or that any function whose domain is a discrete topological space is continuous. Does ArbCom really want to codify which deductions require reference to published sources and which don't? Geometry guy 02:52, 14 March 2011 (UTC)

Our aim is to reflect sources - I guess I always take it to mean thus...I am actually trying to think of an instance where I've done any mathematical inference while writing....and I can't. Casliber (talk · contribs) 03:32, 14 March 2011 (UTC)

People use mathematical inference (sometimes erroneously) all the time often without realizing it. In this edit for example, you did not feel the need provide a source for the rarity of cultivation being a consequence of the difficulty in propagation. Instead you added further reasons for the difficulty in propagation, which support the implicit logical connection. This is not a shining example, but I took it right from the top of your contribs, without even trying to find anything better. Geometry guy 03:59, 14 March 2011 (UTC)

Hmm, the source I added afterwards covers all three points. Hence I didn't have to infer anything as the inference was already covered in the original source. The first sentence I added and only added the second when I had a source (I knew it anyway as this plant is so damn hard to propagate espite growing in bushland everywhere :((( ) 04:32, 14 March 2011 (UTC)

I thought it might, but didn't have access to the source: you are smart enough to say "all three points", so it would be a great pity if you have never made a logical inference in your contributions! Geometry guy 07:59, 14 March 2011 (UTC)

(←) Fortunately you do (at least I hope so, per above!). I went back not much further, and found this edit: where the source has "The Vaucluse estate had been unoccupied since 1898... He bequeathed... the remaining estate to his wife Sarah that, upon her death in 1880, passed to their sole surviving unmarried daughter, Eliza Sophia Wentworth. Following Eliza’s death in 1898 the estate reverted to Wentworth’s trustees...", the article has "It was disused since 1898 after the death of Wentworth's last surviving unmarried daughter Eliza Sophia Wentworth". This contains implicit inferences: "sole surviving" implies "last surviving" (a logical triviality), and "unmarried in 1890" plus "no heirs in 1898" implies "unmarried in 1898" (some minor but reasonable assumptions). (There are some even more minor assumptions, such as dead people not having new children, even the "long-lost" variety!)

You may not find this example terribly compelling either, and may be able to reword the sentence so that it does not imply anything which is not in the source or William Wentworth. I'm not trying to find particularly good examples, nor "prove you wrong", but to illustrate the natural and desirable process of thinking while editing. This is an encyclopedia, and to stay on-topic often requires summarizing sources, combining them in a sensible (e.g. historical) order, and other routine logical manipulations. It is good that editors engage their brain while editing. Sometimes they get it wrong, and introduce original synthesis in the process, but routine manipulations of source material extend far beyond arithmetic. Geometry guy 20:33, 14 March 2011 (UTC)

Arithmetic?

Why is the word "arithmetic" used in the routine calculation proposed finding? There are many types of routine mathematical calculations that are not arithmetic in nature (alphabetizing a sequence of words, for instance, or finding a closed form for an integral of a standard type). It is both standard and good exposition to work through simple examples of mathematical constructions, and this finding would seem to prevent much of that, far beyond its intended purpose within this specific case. It seems a strange, arbitrary, and new restriction, and one at odds with the earlier admonition to keep articles as accessible as possible —David Eppstein (talk) 01:51, 14 March 2011 (UTC)

I doubt many people would consider putting a list of words in alphabetical order to be a mathematical calculation. And if you are finding a closed form for an integral of a standard type, without it appearing in a textbook somewhere, then that is original research. I didn't make WP:OR up, I just quoted from it. --Elen of the Roads (talk) 01:54, 14 March 2011 (UTC)

If you are following a cookbook method for the closed form of an integral but the exact integral you're doing isn't one already worked out in the textbook for you, it's not original research, it's an exercise. And alphabetization could easily be used in an example of a sorting algorithm, which I view as being a form of mathematics. Basically, the statement as it stands seems to be written from the point of view of a mathematically naive reader who thinks that arithmetic is the be-all and end-all of mathematics; it does not make sense for most of our articles on mathematics beyond the high school level. To pick a more advanced example: in Lattice of subgroups there's a section titled "example" which describes all the subgroups of the symmetries of a square. The choice of this group of symmetries, rather than some other group such as the symmetries of a tetrahedron, was not copied from the article's sources, but the listing out of all of the subgroups of this group is, to a mathematician, a routine calculation, requiring no new insights. It's just an example, rather than a theory, and everything in the example is standard. It's intended to make what's in the rest of the article easier to understand rather than to add new theoretical material to it. But the calculations do not use numbers, and they do not use addition and subtraction and the other operations of arithmetic. So your proposed finding seems to prevent this sort of routine use of examples in articles that are about any kind of non-numerical mathematics. And, it's more about what sort of content we should or shouldn't have than I would expect from ArbCom.

By the way, I found this discussion from both WT:WPM and from my own talk page. Many of the WPM participants are fearful that this will lead to the outright elimination of examples from our mathematical articles: we can't copy whole examples from the sources because that would be a copyvio and if this sort of decision goes through we would also be prevented from making up examples. —David Eppstein (talk) 02:36, 14 March 2011 (UTC)

That's my concern as well. This decision would have serious (unintended) consequences if it passed as written and was enforced. I'm sure the intent does not match the wording at present. CRGreathouse (t | c) 02:48, 14 March 2011 (UTC)

Ruling on content is beyond ArbCom's remit (Elen has a more nuanced way to say this, but I can't find the diff right now), so it should suffice to draw attention to the risk of an implicit content ruling. The current arbitration team includes many smart editors. Geometry guy 03:32, 14 March 2011 (UTC)

The intention in the principle is to re-iterate the WP:OR policy, and refers (or should refer IMHO) to novel derivations from first principles. Using substituted figures to illustrate a sourced method is certainly not a novel derivation from first principles, it's just a substitution of the starting point - if I were to write a piece on the standard method for solving simple quadratic equations, I could illustrate it with any quadratic as the method applies to them all. There's nothing novel about it, and I'm not creating any kind of OR with the example.

Glosses may be more challenging - Kiefer Wolfowitz used the example of a gloss for something that has not yet been glossed in sources. I would think this could fall foul of original research as defined by Wikipedia, particularly if the gloss is challenged by other mathematicians. Which brings us to the problem of Monty Hall, and lots of editors providing derivations in their own notation and arguing that others notations are wrong. In that circumstance, since the derivations themselves are contentious, Wikipedia must insist on sources for all the maths.

You guys might like to review the entire of WP:OR to be clear whether or not it presents a difficulty. If the wording here requires improvement, I am happy to put up a variant for the arbs to vote on. This does illustrate why it is better to hash the principles out in workshop first, and I regret that certain other distractions kept me from doing this for all of them. Elen of the Roads (talk) 09:36, 14 March 2011 (UTC)

Coming from a physics background, I'm also very very weary of this ruling. Taking a concrete example from List of baryons, a featured list: the lifetime of resonances is defined as τ = ħ/Γ. where ħ is the Planck constant and Γ the resonance width. Now I needed to list lifetimes (τ) and their uncertainty (Δτ), but this data is unavailable for some of the baryons. However, the information for this exists indirectly, in the form of resonance widths (Γ ± ΔΓ), rather than lifetimes (τ ± Δτ). Converting width (Γ) to lifetime (τ) is simply punching numbers through τ = ħ/Γ (this can easily be sourced), but to convert uncertainties requires a bit more effort and some knowledge of differential calculus. One first needs to derive, from first principles, the uncertainty relations (which, after you do the basic calculations, turns out to be Δτ = ħΔΓ/Γ²). Now that second part is obvious to me, is obvious to any physicist working in the field, should be obvious to any physicist or mathematician (or anyone actually) capable of doing basic calculus, and is completely uncontroversial. However that second part is also, as far as I'm aware, unsourcable to the degree which ARBCOM seems to want to require from now on.

This is a ruling on content, which quite frankly, ARBCOM is utterly unqualified to make. Case in point, most ARBCOM members are probably confused by the math I just gave, yet this is something that would be understood by anyone who passed a basic calculus class. 09:46, 14 March 2011 (UTC)

It's not a ruling on content at all. No original research is one of the pillars of Wikipedia, and this is a straight quote from it. Elen of the Roads (talk) 09:57, 14 March 2011 (UTC)

I fail to see where in WP:OR and particularly in WP:CALC the words "... deriving mathematical results from first principles, without reference to a published source, constitutes Original research within the definition used by the English Wikipedia" or "... deriving mathematical results from first principles, where the derivation hasn't been published in a reliable source, is original research within the definition used by the English Wikipedia" appear. Headbomb {talk / contribs / physics / books} 10:09, 14 March 2011 (UTC)

It fairly clearly excludes the type of calculation that you wish to do, and that's not going to change any time soon, regardless of this case. If you want to add the uncertainties, you will have to persuade someone to publish a table of them. Elen of the Roads (talk) 10:23, 14 March 2011 (UTC)

And it is precisely what is wrong with what ARBCOM proposes, because this stuff is both utterly trivial to perform and non-controversial (and well-within the current WP:CALC), and no one at WikiProject Physics would object to include derived uncertainties on grounds of "original research". Headbomb {talk / contribs / physics / books} 10:45, 14 March 2011 (UTC)

The (Bayesian posterior/consequent) probability intervals can be derived using the change-of-variable formula (Radon-Nikodym theorem), just as one can derive 2372+1=2373 using arithmetic principles (which can be challenged and then can be sourced). We cannot always source trivialities such as 2372+1=2373. Such derivations are trivial for mathematicians (not necessarily logicians!). Such derivations are obvious and never a subject of argument. They should be recognized as important for exposition and protected from challenges as "original research by synthesis".

Mathematicians disagree sometimes on the best way to present material: Criteria include simplicity, generality, insight/surprise, accessibility, relations to other topics. Articles are linearly ordered, and choices must be made.  Kiefer.Wolfowitz  (Discussion) 10:37, 14 March 2011 (UTC)

Hard cases make bad law. Several policies and guidelines such as WP:NOR already exhibit the problem that they only make sense in contentious situations and therefore have to be routinely ignored. Prescribing and fixing an interpretation of NOR as it applies to a specific class of articles will exacerbate the problem unless done with extreme care. There is a reason the mathematics project is extremely concerned:

• Mathematics articles differ from most other articles in that to a large degree they must teach rather than just inform. (This difference between mathematics articles and most other articles is necessary and not specific to Wikipedia. It reflects special features of mathematical literature and of mathematics education at all levels.)
• The main complaint about mathematics articles, and apart from the Monty Hall Problem article and very occasional cranks or self-promoters very much the only contentious issue for mathematics articles is that they tend to be very hard to understand for laypeople.
• Making mathematics articles more comprehensible requires the crafting of examples that fit the articles and therefore may not be in the literature. Just copying examples from the literature is a lazy practice that comes very close to plagiarism, even when a source is given, in those cases in which examples are practically arbitrary.
• It's extremely tedious and useless work to scour through an extensive didactic literature just to find an obvious example that anyone who knows the field could make up in two minutes. At the other extreme, for many advanced articles such a didactic literature does not exist yet and we would be forced to keep articles unnecessarily technical, essentially parrotting our sources instead of adapting them to our genre (that of an encyclopedia).
• Proposed decision 11 does not just say what NOR says anyway. In a subtle but important way it is considerably stronger.

• NOR: "This policy allows routine mathematical calculations, such as adding numbers, converting units, or calculating a person's age, provided editors agree that the arithmetic and its application correctly reflect the sources."
• Proposed decision: "Routine arithmetic calculations, such as adding numbers, converting units, or calculating a person's age are permitted within articles. However, deriving mathematical results from first principles, without reference to a published source, constitutes Original research within the definition used by the English Wikipedia."

Under the standard interpretation of NOR, it is no problem to make up example sentences for a linguistics article, as it is analogous to routine mathematical calculation and not contentious. The proposed new interpretation outlaws non-arithmetical mathematical calculations even though they are analogous to arithmetical calculations, and does so even when they are not contentious. A fortiori this brands the two examples in English relative clauses#Restrictive or non-restrictive as original research -- unless they have all appeared literally in a source. Hans Adler 10:45, 14 March 2011 (UTC)

Hans - I'm not trying to expand on what's in OR, but that does seem to say that only trivial calculations are allowed without source. I entirely agree with the point about examples, to my mind, substituting one example for another example of the same thing to avoid a copyvio is not original research. Can you think of better wording, and let's put that to the committee? Elen of the Roads (talk) 12:44, 14 March 2011 (UTC)

I believe the NOR policy started with the principle "Wikipedia is not a place for cranks to advertise their theories" (someone correct me if I'm wrong, this was before my time here), but gradually became broader and broader to the point that it is now hard to tell the difference from WP:V. At the moment it's about as extreme as it's going to get. It has certainly crossed the point of diminishing returns. There is a lot of fine-tuning going on. E.g. occasionally it is proposed to extend the routine calculation exception explicitly to elementary logic. (This is problematic because outside very formal contexts, "Every A is B." and "Every B is C." does not automatically imply "Every A is C" for the simple reason that "B" can mean slightly different things in the first two sentences.)

This is not a non-negotiable fundamental principle of Wikipedia. It is one of those rules that must perpetually be tuned so that they are a net benefit, and sometimes must be changed in response to new trends and fashions in our community. The current text says "routine mathematical calculations". A year ago it said "routine calculations". If anyone wants to change this to "routine arithmetic calculations" then this change should be proposed and discussed at WP:NOR, not in an Arbcom decision. This is simply not the right forum for twiddling policy in this way, and I am also worried because Arbcom caselaw tends to have more inertia than written policies. If anyone starts abusing the wording proposed here, a consensus at WT:NOR will not be enough to stop this. Instead, another Arbcom case or at least motion will be required. Hans Adler 15:20, 14 March 2011 (UTC)

I thought it said 'arithmetic', but on checking it says 'mathematical' and then goes on to state that there must be a consensus that the arithmetic is correct. I can't see it makes the slightest difference - it is plainly only talking about a dispensation to do some easy sums. At the same time, most of the maths on wikipedia is surely sourceable if anyone asked - it's in textbooks and such. We surely do not have someone solving Fermat's last theorem on article talkpages. The only requirement is that there is a source in back of it. Using a textbook to elucidate the steps in a proof is not WP:SYN. --Elen of the Roads (talk) 16:04, 14 March 2011 (UTC)

The meaning of original research

I think that most of the concern on this topic amounts to a concern about the meaning of the phrase "original research". WP:NOR says that original research is material not originally published by reliable sources. But what counts as material? A very strict reading could argue that every sentence original to Wikipedia represents an original thought, and therefore counts as original research or synthesis. A slight rephrasing of a reliable source's sentence might change the original emphasis or alter some shade of meaning, and the only way to ensure that Wikipedia's sentences are totally devoid of original content is to copy them straight from something else, that is, to commit a copyvio.

WP:NOR goes on to say that copyvios are prohibited, and that "Articles should be written in your own words while substantially retaining the meaning of the source material." Because this permits slight shifts in meaning, it allows slight amounts of original research. What is not permitted, and what the policy spends most of its time discussing, might be called original ideas. If I have a brilliant new idea for a revolutionary new theory, I can't go straight to Wikipedia. But brilliant expository prose is always welcome here (as far as WP:NOR is concerned; there are other restrictions).

What I am concerned about, and what I think most of the mathematics WikiProject is concerned about, is whether unpublished but well-known or easy mathematical reasoning counts as original ideas or not. Everyone agrees that arithmetic is not an original idea. Even if there are no reliable sources for 2974561 + 923592 = 3898153, this computation is not original enough to be the kind of original research we are worried about. A claim that 1 + 1 = 3 would be too original to include without a reference. In between is something like the example I wrote (based on an earlier version of the article) at Chain rule#First example. This is a straightforward first-semester calculus exercise. It is certainly unsourceable: The chances that someone else has written down this exact same exercise with the exact same numbers and the exact same setting are effectively zero. And it is certainly not arithmetic. But any good calculus student can do this problem (those of you who never took calculus or who took it years ago are excused). It has effectively no new content. However, the proposed findings of fact may prohibit it. While I do not think that this example is a derivation from first principles, it is closer to that than to arithmetic.

I suspect it is necessary to impose very strict, straitjacketing restrictions on Monty Hall problem. But I would like to plead that such restrictions not be placed, even implicitly, on other mathematics articles. Ozob (talk) 12:48, 14 March 2011 (UTC)

I do see the concern of the maths community. Your calculus problem is the equivalent of someone editing a linguistics article and adding a new example of Litotes to avoid a copyvio - the method (the definition of litotes or how to do the calculus) is very well referenced, the editor has just slotted some different variables (phrases, numbers, symbols) into the referenced method. This isn't what is meant here - the problem lies where the outcome is novel and/or controversial. I suspect the Bayesian formulations in Monty Hall were unproblematic - it was the differing interpretations of the problem/solution that they were being used to support that was the issue, and in such a melee, one really does have to go back and say "sourced information only". Elen of the Roads (talk) 13:41, 14 March 2011 (UTC)

So mathematicians are allowed to perform basic calculus, but not physicist??? Headbomb {talk / contribs / physics / books} 17:56, 14 March 2011 (UTC)

The difference is that the mathematicians want to demonstrate how a calculus problem is solved, without slavishly copying the textbook example which would result in a copyvio. What you want to do is put up a table of results of your offwiki calculations. If challenged, the mathematician can point to the calculus textbook and say "here is where it shows how to do this calculus". Where are you going to say you sourced your results from? Elen of the Roads (talk) 18:04, 14 March 2011 (UTC)

Yes -- exactly! The concern is that the text, as written, might be misunderstood as prohibiting that sort of routine manipulation. I'm not worried about ArbCom so much as a well-meaning editor who comes across the finding without understanding this nuance. CRGreathouse (t | c) 14:30, 14 March 2011 (UTC)

I am open to suggestions as to a more effective version of the principle. It is not intended to establish anything new, just describe things as they are. Elen of the Roads (talk) 15:21, 14 March 2011 (UTC)

I still don't understand why the Arbcom needs to make general statements on what constitutes original research in mathematics at all. Imho all that is required here, are specicific assessments, whether any of the involved parties engaged in OR or not based on current policies. This is less than offering an own rewording of the general policy, for which this here is the wrong forum as Hans Adler has pointed out above correctly.--Kmhkmh (talk) 15:47, 14 March 2011 (UTC)

Arbcom would normally make a statement on current policy before making a statement that editor Foo has violated current policy. If the statement needs to be more nuanced, suggest more wording because you guys clearly think this is saying something different to the OR policy. Elen of the Roads (talk) 16:09, 14 March 2011 (UTC)

Richard D. Gill

In the real world, Richard D. Gill has been involved in legal proceedings, by writing papers and by being interviewed by the news media. Extra care should be taken to avoid harming his reputation here, lest a wrongfully convicted person have less access to an honest expert witness or news reporters question his motives. It seems to me that he is being banned from the MHP for one year at his own request, as his sacrifice to WP to make the page open and inviting for new editors.

I don't understand why there is a discussion of his being stimulated by the WP article to write original research publications, which (after all) can be included once they meet the standard of reliable sources. Perhaps he may have been too enthusiastic on talk pages a few times, but it does not seem to me that he has added content without substantial support and acknowledgment from some other editors. The present language could be used to smear Professor Gill as manipulating WP to serve his own ends, contrary to the facts. In fact, Gill's contributions to WP continue to be made at great sacrifice to his academic research. I would suggest omitting the statement about his original research, and underscoring that Gill requested his ban, to send a signal to the WP community (and beyond) that new editors are welcome on the MHP.  Kiefer.Wolfowitz  (Discussion) 09:30, 14 March 2011 (UTC)

Kiefer, writing papers and being interviewed by the press does not constitute being involved in legal proceedings. That requires a court, writs, judges etc. Wikipedia is certainly not a court, and it is well understood in the media that it is possible to conflict with Wikipedia's rules and end up prevented from editing an article, without it being a comment on one's character. What he has done (WP:COI issues arising from closed loop referencing) is a very technical offense against one of Wikipedia's more arcane rules. I don't think that talk of convictions, smears and harm to reputation is particularly helpful here. --Elen of the Roads (talk) 09:41, 14 March 2011 (UTC)

Hi Elen! I could not find a subsection on closed-loop referencing on the COI page. Thickly,  Kiefer.Wolfowitz  (Discussion) 11:19, 14 March 2011 (UTC)

Closed loop referencing. You want the article to say some X. You are in a position where you can get a paper published saying X. You then come back to the article and add X as a source. The correct approach would be to suggest to other editors that they may find your paper useful, and wait for them to add it. It's a very technical contravention - the information has been peer reviewed so I presume it is sound, it's only to do with how the community prefers to handle experts who come with their own references.Elen of the Roads (talk) 12:49, 14 March 2011 (UTC)

Your explanation was clear and helpful. The COI-policy recommendation that researchers propose additions of their results on talk pages then covers the problem with Richard adding such references himself. Thanks for your explanation!  Kiefer.Wolfowitz  (Discussion) 12:54, 14 March 2011 (UTC)

I struck through the unhelpful comments. You are welcome to remove such comments & your response if you like.  Kiefer.Wolfowitz  (Discussion) 10:04, 14 March 2011 (UTC)

No worries. Did you mean "called as an expert witness in legal proceedings"? I wasn't aware he was actually called into court. I thought he just advised. Elen of the Roads (talk) 12:56, 14 March 2011 (UTC)

I believe that Gill wrote on the talk page for the article about himself that he has not appeared in court for the Lucia de Berk case. However, he could appear as an expert witness in the USA, in some possible world. The statistician David A. Freedman was an expert witness for many cases. My concern about his reputation being questioned by an opposing lawyer derives from my legal expertise (entirely gained from viewing Law & Order!). Sincerely,  Kiefer.Wolfowitz  (Discussion) 13:18, 14 March 2011 (UTC) 16:25, 14 March 2011 (UTC)

I have been a court witness in legal proceedings. In fact, concerning statistical analysis of DNA profiles. Also in several litigation cases about correlation versus causation. Honestly I don't think I produced any new ideas on MHP: every single idea I came up with myself, or learnt from a fellow editor, turned out to previously exist in a reliable source. Just as one would expect. The way I am used to editing maths and statistics articles on wikipedia is that everyone composes nice examples of existing results, and nice ways to understand existing results, and everyone helps one another improve these, find references if possible, or remove if people find it unnecessary or unuseful. When I add some text to MHP I expect constructive camaraderie. Fine by me if no one likes the addition, they say so, and it goes again. Now it's amazing that when I correct blatant wrong notation, someone screams blue murder. I can give references to "usual notation" if necessary. I think that in such a case, I am correcting someone else's bad OR. Whoever wrote out those lines of formulas certainly can't have copied them from a textbook. Moreover they clearly had no idea what they had written: it was gobbledygook. Richard Gill (talk) 16:17, 14 March 2011 (UTC)

That's precisely what I'm trying to get at with the OR thing. BTW, given Kiefer's laudible concern, I am happy to make clear that any sanctions are for what one might term 'etiquette problems', not for inserting dodgy statistics. Elen of the Roads (talk) 16:28, 14 March 2011 (UTC)

Just to reassure you all: it is fine by me to be told off for "closed loop editing". And fine for me to let the dust settle for a year and let other people do what they like with my published writings (including ignoring them). -- Though if this was an issue, I don't see why another editor didn't remove the text or reference. That so-called "O.R." contained nothing new, everything is sourced, it just collected known facts which I learnt from fellow editors at wikipedia (whom I collectively thanked) in a convenient package and added some personal opinions about teaching probability and statistics and the dangers of solution driven science. And those opinions were *not* referred to by myself or anybody else on the MHP page.

I share the concerns of other editors who like to write on maths, that taking the rule "no new maths beyond elementary arithmetic" literally would destroy any of our inclination to work on Wikipedia. We could better work on citizendium.org or statprob.com, where there's a degree of peer-review and professional collegiality. And then Wikipedia editors can just copy our citizendium / statprob articles. Obviously the writers themselves aren't allowed to do that. And what's the fun of copy and paste?

So there is a big problem with articles on subjects where there is both a big technical literature, and a big popular literature. Personally I think it is a really big challenge to bridge those worlds. That's what I have to do in my work on forensic statistics. It's an unsolved maybe insoluble problem. MHP is a great testing ground for this. Richard Gill (talk) 16:44, 14 March 2011 (UTC)

WP:OR and WP:V haven't changed dramatically in the last few years - the thing seems to be that the mathematicians have ignored it. The principles should encapsulate existing practice, not be new practice - unless the maths community can come up with some wording which encapsulates what they do and shows what the problems with Monty Hall were, we have to go with what the policy states, since that's what people are supposed to be doing.Elen of the Roads (talk) 16:51, 14 March 2011 (UTC)

I think the existing policies are actually quite sufficient. WP:OR says no original research. WP:V says what needs to be sourced isn't everything, but only quotes and content challenged or likely to be challenged. What the math folks are saying is there's way more than "simple arithmetic" that would not be considered to be OR and that no one would challenge. The bright line is whether something is challenged. So, include whatever intuitively obvious results you want - but if what you say is challenged either provide a source clearly showing what you're saying is not OR or get a consensus of editors to agree the challenge is baseless. -- Rick Block (talk) 17:23, 14 March 2011 (UTC)

No, that's not what WP:V says. It says that you must be able to provide a source for material if asked for it. You don't routinely have to source 'humans are air breathers' because no-one challenges it. If it is challenged, you have to provide sources - there's no 'consensus of editors to agree the challenge is baseless.' Elen of the Roads (talk) 17:35, 14 March 2011 (UTC) ETA all material added to articles must be attributable to a reliable published source, even if not actually attributed <-- features in both WP:V and WP:OR. There may well be no need to actually cite the textbook if no-one challenges it, but the source has to be there. Elen of the Roads (talk) 17:40, 14 March 2011 (UTC)

What I mean is that a challenge of a basic math result, like 1+1=2, (as opposed to a challenge of a "fact") can be satisfied by a consensus of editors concluding the challenge is baseless - i.e. not all citation requests are reasonable and whether they're reasonable or not should be a consensus decision. -- Rick Block (talk) 17:58, 14 March 2011 (UTC)

IMPORTANT: Richard, you have stated that you inserted references to your own papers in the article only where the results are due to others (and are cited in your paper). Is that correct?

Does ArbCom agree?  Kiefer.Wolfowitz  (Discussion) 17:16, 14 March 2011 (UTC)

*All* the mathematical results in those papers are attributed to earlier writers. The opinions are my own. Some results are extracted from other writers' proofs. For instance, a writer assumes A, B and C. Then uses A only to establish D. So I wrote A implies D and cited that writer. An editor who by their own admission can't read elementary (high school) probability theory disputed my claim on the talk page that A implies D (citing author...). So what could I do but write it out and get it peer reviewed? That was fun. (Is this what is called making a"gloss")? Later an editor disputed my reading io Rosenthal's paper. An expert from my own field writing for a professional audience. After many failed attempts to explain, I wrote to Jeff R., who was more than happy to be quoted that my reading was correct.

As to the history of the citations, first they were references by me on the talk pages to my preprints on arXiv.org or on my homepage in Leiden. When they were published, I updated the reference. I have no idea whatsoever who moved such a reference from the talk pages to the article. As far as I am concerned this was all done in an atmosphere of collaborative editing and service to the community. And obviously the citations are superfluous since the so-called "O.R." was not new mathematics. This is not like a Pratt and Whitney engineer designing new rotor blades! However, a non expert can hardly see the difference. It's abracadabra. Weird symbols and words. A high priest making incantations to the spirit world in a secret language. Richard Gill (talk) 17:46, 14 March 2011 (UTC)

I agree there's nothing novel in Richard's papers. So, essentially anything referenced to his papers could be referenced to some previous source. I mean, lets think about this. There are hundreds (maybe thousands) of previous sources about the MHP. The chances of anyone coming up with something novel at this point are very small - and if they do, the chances that whatever it is belongs in this article is within a small epsilon range of 0. -- Rick Block (talk) 17:58, 14 March 2011 (UTC)

IMHO, some rephrasing of the findings about Richard then seems desirable. He has already expressed being treated differently on WP in recent weeks, and the current wording may intensify such injustices. (I believe that the committee understood Richard to have introduced some fairly minor results in the article, rather than reporting others' results.)  Kiefer.Wolfowitz  (Discussion) 18:30, 14 March 2011 (UTC)

Probability theory falsehood

The Monty Hall problem (MHP) is not a problem of probability theory, as erroneously asserted in the finding of fact. It is a problem of statistical decision theory, which concerns economics, statistics, and philosophy as well as mathematical probability theory. Jeff Rosenthal does not make major mistakes about probability. Probabilists and statisticians do make obvious mistakes frequently about statisticial decision theory, simply because of ignorance about elementary distinctions between probabilities of conditional (if/then) events and conditional probabilities, or about probability kinematics (Jeffrey's rule), etc.  Kiefer.Wolfowitz  (Discussion) 12:29, 14 March 2011 (UTC)

Proposed finding:

Inspired by a popular game show, the Monty Hall problem (MHP) started life as an example of probability theory statistical decision theory, intended for students and the wider public. Since its publication, it has become an example of optimal decisions under uncertainty, which concerns probability theorists, statisticians, economists, and philosophers. On Wikipedia, the editing of the article on the MHP has featured disagreement over how to present the various forms of both the question and the answer, so as to provide complete coverage of all the facets of the problem, without overwhelming the general reader.

No. It's close enough as it is. The finding does not commit the problem to be one thing or another. --Elen of the Roads (talk) 13:19, 14 March 2011 (UTC)

Richard Gill just made a similar not dissimilar comment as mine, above.  Kiefer.Wolfowitz  (Discussion) 16:06, 14 March 2011 (UTC)

Read what he said more closely. Elen of the Roads (talk) 16:29, 14 March 2011 (UTC)

My providing the link to Richard's diff was meant implicitly to encourage others to read his original words (noting any differences). Thanks for making such caveat lectors explicit!  Kiefer.Wolfowitz  (Discussion) 17:18, 14 March 2011 (UTC)

Original research (Mathematics)

I share some of the concerns above and I wonder a bit why we would need such a section with a general claim at all? This case started out as problem between editors on very specific chronically problematic article of relatively low importance and it should not have a side effect for math or science articles in general, in a particular since this is happening largely out of sight of the involved communities. Is there an option to explicitly tie any assessment in that area to the MHP alone, to avoid that this is becoming a ruling seen as a general guideline?--Kmhkmh (talk) 13:07, 14 March 2011 (UTC)

You mean the original research is going on out of sight of the community? The plain fact is that everything on Wikipedia must be verifiable in published sources. We wouldn't allow an engineer from Pratt & Whitney to write an article on how some new fangled type of jet engine works without he provides some published sources, we wouldn't allow a leading economist to post a novel way of explaining where all the money goes in a recession without he provides some published sources. --Elen of the Roads (talk) 13:29, 14 March 2011 (UTC)

I'm not sure what you are talking about know, since this has nothing to do concerns raised above. The issue is here what exactly gets considered as novel or actual research in the math domain (i.e novel for who). Of course we won't allow publication of novel theorems, concepts or definitions in WP, the issue is here, that "novel" or "knowledge likely to be challenged" depends on the perspective and domain knowledge. And we want to avoid having articles tagged as unsufficiently sourced over even content removed, which anybody with domain would consider as sufficiently sourced and/or "obviously" true. And yes every piece of information needs to verifiable, but the questions is again by who (i.e. somebody with (some) domain knowledge or all/the average reader). Imposing the latter is often impractical in science or math articles and blocks desired practices (such as providing examples).--Kmhkmh (talk) 14:54, 14 March 2011 (UTC)

By a consensus of editors. That is the only criterion that can be applied. --Elen of the Roads (talk) 15:19, 14 March 2011 (UTC)Struck this - realised I didn't quite answer the question you asked. The answer to 'who needs to verify the information' is that the consensus of editors on the talkpage need to agree that the source your provided verifies the assertion. The rule in WP:V isn't different for mathematicians. Elen of the Roads (talk) 18:08, 14 March 2011 (UTC)

Indeed. So if there is a discussion between laypersons and experts, and it turns out that something that the experts all know isn't written down clearly in a way that the laypersons can recognize, the expert has no option but to write it on his university home page or blog or publish in some professional recreational / pedagogical / opinion venue, point this out on the talk pages, and take a back seat. As long as the editors of specialist math articles have consensus, they do not have to worry about OR. The definition of OR is that which is challenged, not that which can be challenged. The mathematicians will continue to work within the spirit of the law. Was it the State of Nevada that ruled that pi is 22/7? Richard Gill (talk) 17:14, 14 March 2011 (UTC)

I think that's pretty much it. I don't think you guys are really conducting much original research - if push came to shove you could say "well it's in Foo - the definitive text for calculus" or whatever. You just don't often use sources because everybody knows it's right anyway. If you really do have the solution for whatever is the next Fermat's Last Theorem, you'd be publishing it elsewhere anyway. The problem is where a fight breaks out and you all start favouring your own derivations, instead of going back to the sources specific to this problem. Elen of the Roads (talk) 18:13, 14 March 2011 (UTC)

Repeating my opinion from the math project page: The behavioral problems with the talk page are to blame. It is not clear that a statement of mathematical policy is needed, unless another math article ends up here and is free from behavioral problems. Again, I am sorry for sounding opinionated,  Kiefer.Wolfowitz  (Discussion) 18:40, 14 March 2011 (UTC)

"Article has been subject of original research"

I don't understand this proposed finding of fact, at least not as related to the claimed reference [2].

5) The talkpage, and at times the article, has contained a considerable amount of derivation from first principles, in an effort to explain the higher aspects of probability theory

Firstly, this isn't original research. It's the straightforward calculation that any Bayesian analysis of the problem is going to do. For example, here it is on page 60 (equations 3.36 to 3.40) of David MacKay's well known book on Inference and Information Theory. Any other book or paper that presents the problem from a Bayesian angle will replicate it.

Indeed, the exact same calculation was already in the article as of that edit, in the section Bayesian analysis; and it's in the article right now, at Monty_Hall_problem#Mathematical_formulation, just where Nijdam in this edit wanted to put it.

One can quibble about the presentation -- the very telescoped presentation in Nijdam's edit isn't particularly easily presented, nor did he introduce the material as straightforwardly as either the section "Bayesian analysis" that was already in the article when he edited it, or the section at "Mathematical formulation" in the current article. And it's not helped by the fact that he didn't really explain his notation.

But putting that to one side, let's look at what we've got here for the purposes of WP:OR:

• (1) Stating the previous word assumptions in mathematical terms, using mathematical variables. -- Per all policy, simply choosing a particular set of mathematical variables to express the problem is not OR. The way Nijdam sets things out isn't particularly elegant or well explained or beautifully typeset, but it's not wrong.
• (2) Application of Bayes' Theorem. This is the standard way to solve the problem in a formal mathematical way. Its use here is absolutely uncontroversial. If the question was just to demonstrate quickly where the number 2/3 came, this wouldn't normally make anyone bat an eyelid. (But see point 4 below).
• (3) The calculation itself. This is just simple arithmetic, no more than saying 127 + 1 = 128. Bayes' rule is a sausage machine -- you put in the numbers, turn the handle, out comes the answer. Now I think the guys further above on this page have a point, that the word "arithmetic" in the proposed statement of principles is far too narrow -- it's not appropriate to forbid basic calculus, or basic algebra, when these are at a level appropriate to the article. But even if we were to make that prohibition, and restrict what is allowed to arithmetic, this is arithmetic.
• (4) Presenting this as a way to think about the problem. This article is somewhat unusual, because the spine of it is "how to think about the question". Since what was being added in this edit was a way to think about the question (rather than just motivating where a particular number comes from), arguably it could to be said to be "presenting a position" per WP:OR, which should be attributed. So it would have been good to incorporate an attribution to RSs presenting this approach. But it seems to me that that omission was at most a solecism. The principle of the calculation was not controversial; indeed it was already part of the article, in the "Bayesian analysis" section, with a cited reference (Gill 2002). As it was already there in the article, Nijdam can hardly be said to be contributing "original research", merely by presenting it in a different way.

As a footnote, it is maybe worth pointing out that the controversy in the Monty Hall problem isn't about the mechanics of the calculation -- that is just the application of a basic theorem in probability. On the other hand, there is some controversy as to what are the numbers you should throw into the sausage machine.

In Nijdam's notation, this is the conditional probability rule P(H=2|C=3)=1, P(H=3|C=3)=0 which is simply a mathematical statement of what is drawn in the picture above. This assumes that the host knows where the car is, and will avoid it if he can. If this is accepted, then from this follows inexorably the result that what might all too easily be dismissed as apparently irrelevant information is in fact very relevant: i.e the guest should switch.

On the other hand things can be muddied if people think that the host has no idea where the car is, and might as easily have opened the door that did have the car behind it. In Nijdam's notation, this would correspond to the conditional probability rule P(H=2|C=3)=0.5, P(H=3|C=3)=0.5. If you threw those numbers into the Bayesian sausage machine, you would get out a different answer. But that was not what was shown in the picture, so Nijdam was right not to have presented it.

But that's a digression. Bottom line, it seems to me, is that given what was already in the article, what Nijdam added was not original research, so should not be identified as such as a finding of fact. Rather, it was a re-presentation (and duplication) of material that was already in the article, where it was already quite properly sourced. Jheald (talk) 19:18, 14 March 2011 (UTC)

I'm also puzzled by the mention of the talkpage in the proposed finding of fact. Why is this relevant? Talkpages aren't limited by WP:NOR. Indeed it can often be very useful for editors to set out personal understandings, to iron out misconceptions and get everybody onto the same page. Jheald (talk) 19:28, 14 March 2011 (UTC)

Arbitrators opinion

The statement of dispute is the arbitrator's opinion of the statement of dispute. It doesn't have to be neutral, balanced, or use any of the words that you guys want it to contain. Not even one. It doesn't even have to be what you think the issue is. What it says is what we the arbs think. If we want to word it in simple language, that's how it will be worded. Also, it doesn't really matter - it's only there for us, and for any casual observer, who might look and say "what was all that about then". It doesn't have to be mathematically correct to the 99th quartile or whatever. So you can all stop trying to persuade me to rewrite it :) :) --Elen of the Roads (talk) 19:53, 14 March 2011 (UTC)

"Higher" probability theory

eg:

the problem and solution as presented in higher probability theory (from "Statement of dispute (two camps)")

in an effort to explain the higher aspects of probability theory (from "Article has been subject of original research")

Notwithstanding what you've just posted, this language is an embarrassment to you and should be revised. Bayes Theorem is not "higher probability" -- it is basic, introductory stuff. Describing it as such makes you sound like a gaggle of Victorian spinsters: "ooh... maths... frightening".

As an alternative form of words perhaps "a more formal approach based on conditional probability" might be appropriate? Jheald (talk) 20:01, 14 March 2011 (UTC)

I could replace it with 'bloody complicated maths stuff' if you like :) Seriously, for most people who don't frequent a bookmaker, all probability is scary maths stuff, and Bayesian notation really is rocket science. --Elen of the Roads (talk) 20:26, 14 March 2011 (UTC)

As probability theory goes, it is the basics of the basics. —David Eppstein (talk) 20:30, 14 March 2011 (UTC)