Wikipedia:Arbitration/Requests/Case/Monty Hall problem/Evidence

Anyone, whether directly involved or not, may add evidence to this page. Create your own section and do not edit in anybody else's section. Please limit your evidence to a maximum of 1000 words and 100 diffs. Giving a short, concise presentation will be more effective; posting evidence longer than 1000 words will not help you make your point. Over-long evidence that is not exceptionally easy to understand (like tables) will be trimmed to size or, in extreme cases, simply removed by the Clerks without warning - this could result in your important points being lost, so don't let it happen. Stay focused on the issues raised in the initial statements and on diffs which illustrate relevant behavior.

It is extremely important that you use the prescribed format. Submitted evidence should include a link to the actual page diff in question, or to a short page section; links to the page itself are insufficient. Never link to a page history, an editor's contributions, or a log for all actions of an editor (as those will have changed by the time people click on your links), although a link to a log for a specific article or a specific block log can be useful. Please make sure any page section links are permanent. See simple diff and link guide.

This page is not for general discussion - for that, see the talk page. If you think another editor's evidence is a misrepresentation of the facts, cite the evidence and explain how it is incorrect within your own section. Please do not try to refactor the page or remove evidence presented by others. If something is put in the wrong place, leave it for the Arbitrators or Clerks to move.

Arbitrators may analyze evidence and other assertions at /Workshop. /Workshop provides for comment by parties and others as well as Arbitrators. After arriving at proposed principles, findings of fact or remedies, Arbitrators vote at /Proposed decision. Only Arbitrators (and clerks, when clarification on votes is needed) may edit the proposed decision page.

Evidence presented by Glkanter

 *  My entire section of evidence and responses can be read here. Glkanter (talk) 02:13, 21 February 2011 (UTC)

The overriding POV of the current article, as promoted by Rick Block and Nijdam, is *not* representative of a 'significant minority viewpoint' of reliable sources.
The editors who want an emphasis placed on some 'shortcomings' of the simple solutions are just making it up.
 * "== Conditional vs. unconditional for the umpteenth time =="
 * "(sort of continuing from the ridiculously long thread above) What the most reliable sources about the MHP say is that it is a conditional probability problem. Period. Full stop. There are related unconditional problems, but (IMO) the related problems are distinctly not what most people think of as the MHP or what most people "solving" the MHP using an unconditional solution mean to be solving." Rick Block (talk) 01:57, 14 June 2009 (UTC)
 * "Specifically, unless someone can find a source that defends the validity of an unconditional approach against the published criticisms, e.g. says specifically what unconditional problem some unconditional solution is addressing, or specifically how their unconditional solution addresses the commonly understood conditional problem, the article must not provide any such defense. Lacking any published response (and not just a subsequent regurgitation of an unconditional solution) from the "unconditional side" this is a completely NPOV approach." - Rick Block (talk) 01:57, 14 June 2009 (UTC)
 * "I sincerely hope yuo do not mean by popular literature, the incorrect literature, deceiving the readers. Nijdam (talk) 20:42, 22 February 2011 (UTC)"

As an overwhelming consensus to eliminate the NPOV and other violations in the article was building contrary to Rick Block's preferences, he offered this:
 * "Glkanter asks why I haven't responded about his "Is The Contestant Aware?" question. Why should I? Glkanter has repeatedly demonstrated a complete lack of comprehension of nearly everything I've ever said. It's like trying to explain something to a cat. At some point you just have to give up. However, I'll give it another go. Meow, meeeow, meow, meowww. I'm not sure I have that quite right since I don't speak cat, but it's probably about as comprehensible to him as anything else I could say. - Rick Block (talk) 01:53, 4 December 2009 (UTC)"


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

The only sources that they claim are 'critical' start with a problem statement different than the 'standard' MHP, as per the following table. This includes Morgan, and Grinstead and Snell, both referred to above by Rick Block.

There is no 'significant minority viewpoint' supporting the outlandish claims repeated by these editors. (All references are from the MHP article.) And Morgan, prompted by a letter to their publisher from participating editors Martin Hogbin & Nijdam, has admitted at least one error, and has backed up on their claims.

The sources themselves do not delineate "which" problem they are solving (see Nijdam's OR explanation of the differences). That is also a Wikipedia editors contrivance.

Accordingly, the article should not have the "Simple solutions are wrong" POV it has now, and it would be a contrivance and a disservice to bifurcate the article as if the sources were answering different problem statements. Because they are not.

Posted by Glkanter (talk) 04:32, 20 February 2011 (UTC)

Please note, too, that Selvin, the originator of the puzzle, who gave it the 'Monty Hall' name, and vos Savant, who made the puzzle popular (otherwise there would *be* no Wikipedia MHP article) and responded to thousands of letters, both gave unconditional tables of all possible outcomes as their initial solutions. And never renounced them. Keep this in mind when you read certain editors explaining things like 'intent', and the 'real problem', etc. They are completely contradicting these two fundamental sources. Which I have pointed out thousands of times. So they know it, and they do it anyways. Glkanter (talk) 04:51, 20 February 2011 (UTC)

Response To Rick Block - Glkanter cannot satisfy Verifiability:
[Quoting Rick Block Begins (diffs removed)]
 * ✅ cannot satisfy Verifiability:
 * table "based" on Carlton's solution:
 * Glkanter's "Carlton's decision tree":

[[Quoting Rick Block Ends]

This is nothing more than Rick Block's continuing Gamesmanship and harassment. To see the hypocrisy of his argument, look at this image/table that Rick Block devised. [It is the 2nd (redundant, but my deletion edits are always reverted) image (the one with 21 doors) in the Conditional probability section. There are no sources that present this image.

Arbitration participant Gill110951 disagrees with Rick Block:
 * "My opinion is supportive of Glkanter, though I think his version of Carlton needs some polishing. Decision trees help develop probabilistic thinking. One can give a perfectly good decision tree for the so-called popular solution. That solution is a perfectly respectable (though not unique) solution to a perfectly respectable (though not unique) mathematization of the informal question posed in vos Savant's article, for instance. The MHP is partly such a famous problem because of the richness of thought which it has engendered. The wikipedia page should give an attractive overview, make the maths and logic transparent, bring out the unity of the different approaches, and not dogmatically promote one particular POV. Gill110951 (talk) 17:23, 4 July 2010 (UTC)"

Arbitration participant Martin Hogbin disagrees with Rick Block:
 * "I agree that we should take the host's goat door choice to be uniform at random, regardless of how the host actually chooses, because the player does not know the host policy. These are the reasonable assumption to make and these assumptions are implicit in Carlton's tree.  Thus Carlton's tree shows that a reliable source has made the same assumptions that you and I make but no mathematical solution can prove that those assumptions are correct. Martin Hogbin (talk) 12:32, 8 July 2010 (UTC)"

This is the. It shows that the simple solutions *are* indeed 'conditional', and that a door has been opened, leaving just 2, which some editors insist is the key to many puzzle solvers deriving the incorrect 1/2 & 1/2 response.

This decision tree is derived from:
 * vos Savant's problem statement
 * Various reliable sources giving similar simple conditional solutions
 * Carlton's simple solution
 * Monty Hall's simple solution that Selvin (the problem's originator and name-giver) so effusively praised.
 * Rosenthal's simple solution
 * (optionally) Morgan's (false) Solution 5
 * False? I know. "It's complicated."
 * Countless more reliable sources
 * Mathematics - the multiplicative identity element (multiply by 1)
 * Various Wikipedia policies on visual aids, synthesis, and OR




 * "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?" - vos Savant, Marilyn (1990). "Ask Marilyn" column, Parade Magazine p. 16 (9 September 1990).

"As long as you initially pick a goat prize, you can't lose: Monty Hall must reveal the location of the other goat, and you switch to the remaining door - the car. In fact, the only way you can lose is if you guessed the car's location correctly in the first place and then switched away. Hence, whether the strategy works just depends on whether you initially picked a goat (2 chances out of 3) or the car (1 chance out of 3)." - Carlton, Matthew (2005). "Pedigrees, Prizes, and Prisoners: The Misuse of Conditional Probability". Journal of Statistics Education [online] 13 (2). http://www.amstat.org/publications/JSE/v13n2/carlton.html. Retrieved 2010-05-29.


 *  My entire section of evidence and responses can be read here. Glkanter (talk) 02:13, 21 February 2011 (UTC)

Some background
Monty Hall problem is an FA that has gone through two FARs. Following the first FAR the article looked like this. The "Solution" section in this version, although unreferenced, is essentially vos Savant's solution as published in Parade. Shortly before the second FAR an anonymous user complained about this solution, eventually referring to a peer reviewed academic paper by Morgan et al. that says this solution does not address the conditional probability of winning by switching given the player has picked door 1 and the host has opened door 3 but rather the unconditional probability (effectively the probability before the host has opened a door, but knowing the host will open one of door 2 or door 3). This user's objections to the "simple" solution ultimately led to an RfC, see which ultimately led to this change to the article. Subsequently, in response to the second FAR, numerous changes were made to the article, notably strengthening the referencing and readability changes. Although not an original author of the article, I was the original FA nominator and the primary responder to both FARs, and in response to the second FAR did an extensive amount of referencing work (using both online and printed sources obtained primarily from university libraries).

The "Solution" section of the article following the second FAR still started with vos Savant's unconditional solution, followed by a paragraph clarifying what this solution says ("The reasoning above ..."), followed by a paragraph introducing a conditional solution ("A subtly different question is ..."). These two paragraphs (and other similar content) present as undisputed fact what some editors (primarily user:Glkanter and user:Martin Hogbin) consider to be simply "Morgan's POV", in violation of NPOV. Several editors have argued about this for several years now, progressing through the various dispute resolution escalations to formal mediation. Well before mediation, user:Dicklyon split the Solution section into two sections, one presenting "simple" solutions and one presenting a solution based on conditional probability.

This split has not been satisfactory to a variety of editors, who continue to argue
 * 1) (Martin) Morgan et al. is a deeply flawed source (see User:Martin Hogbin/Morgan Criticism) and any mention of conditional probability should be deferred until after the simple solution and an extensive "Aids to understanding" section is presented
 * 2) (Glkanter) any mention that the "simple" solutions don't quite address the conditional problem where the player has picked Door 1 and has seen the host open Door 3 should be either completely removed or moved to a "Criticism" section at the end of the article.
 * 3) (user:Nijdam) the simple solutions are factually incorrect (Nijdam can identify his real life identity if he cares to, but he is known by all involved to be a bona fide expert in the topic)
 * 4) (user:Gill110951) the "criticism" that the simple solutions do not address the conditional probability is factually correct, but of little importance since by assuming symmetry the conditional and unconditional answers can be proven to be the same. This user is the subject of the Wikipedia article Richard D. Gill and has recently published two papers about the MHP in response to the arguments that have occurred on the article's talk page (and various other pages), and is a co-author of one of the articles that has been a reference in the article for quite some time.
 * 5) (user:Rick Block) there are many sources presenting simple solutions, many sources presenting conditional solutions, and a not insignificant number of sources (like Morgan et al.) pointing out the difference between these kinds of solutions. Per NPOV, all of these POVs need to be in the article but without the article taking sides.

So, what we have here is fundamentally a POV dispute complicated by the fact that the topic is "a simple math problem", and several editors think their understanding or expertise outweighs what reliable sources say.

Glkanter is a disruptive editor and should be at least topic banned
Glkanter exhibits nearly all the classic signs of disruptive editing (see below) and repeatedly disrupts progress.

He is the subject of a previous RFC. All behaviors identified in this RFC have continued unabated. He
 * still edits tendentiously (blocked three times for edit warring, see block log),
 * is still not here to build an encyclopedia (self-admitted SPA, long term history of disruptive behavior with little or no sign of other intentions, treats editing as a battleground , has a complete lack of interest in good editing conduct practices , little or no interest in working collaboratively , long-term history suggesting a marked lack of value for the project's actual aims and methods),
 * still disuptively edits (see below),
 * and still treats editing as a personal wp:battle misusing his user and user talk pages to chronicle his fight and disparage other users.

Signs of disruptive editing (from wp:disruptive editing):
 * ✅ is tendentious:
 * "There is no possible way I am wrong about this", reposted to article talk page, chronicled to his talk page, reposted to Richard Gill's talk page
 * ✅ cannot satisfy Verifiability:
 * table "based" on Carlton's solution:
 * Glkanter's "Carlton's decision tree":
 * engages in "disruptive cite-tagging": - this is one thing Glkanter does not do, although he does the equivalent by repeatedly rejecting references that have been provided for content he objects to
 * ✅ does not engage in consensus building: (isolated comments: ) (thread about a proposed change, progressing until )  (refuses to comment on a proposed change:   )  (exchange where he refuses to say what changes he'd like to see in the article:        )
 * ✅ rejects or ignores community input:
 * his responses to the RFC, ,
 * his response to a mediator's suggestion  to delete a personal attack from his talk page
 * his response to advice about not making personal attacks
 * ✅ campaigns to drive away productive contributors: incivility, personal attacks
 * ✅ refuses to "get the point"
 * recent exchange with Richard Gill:       (exchange continues, ending up with yet another personal attack )

Response to Martin's evidence
Note: this response is to evidence that has since been moved to the talk page .

What the content dispute is about is essentially irrelevant for the purposes of this arbitration. What is at issue here is user behavior, specifically the refusal of some editors (Glkanter is by far the worst, although Martin, Richard Gill, and Nijdam share this to a lesser degree) to let the article represent in an NPOV fashion what reliable sources say as opposed to what these users think about the problem, despite repeated attempts to focus discussion on what sources say, e.g. (far from an exhaustive list).

Martin is simply incorrect about the timing (vos Savant's Parade columns were published in late 1990 and early 1991, the Morgan et al paper appeared in the November 1991 issue of American Statistician - not "ten years after"). He is also incorrect about the "Aids to understanding" section. He moved it. Nijdam immediately reverted it. He moved it again later. I immediately reverted it. He immediately reverted my revert (and I refused to edit war about this but rather discussed it on the talk page ).

The way forward is clear, and it is not what Martin says - it is to scrupulously adhere to NPOV as I've suggested repeatedly, e.g. (not an exhaustive list).

Response to allegations of wp:ownership
I certainly don't deny that I take an interest in this article, but I emphatically deny owning this or any other article. Glkanter first brought this up here, my initial response. Responses from others at the time:.

I generally suggest content changes on the talk page, and do not make changes to the article if anyone objects, e.g.      , and fairly recently successfully engineered a collaboratively edited change to the article while it was protected due to edit warring           (thread continues, eventually resulted in this change to the article). -- Rick Block (talk) 06:17, 19 February 2011 (UTC)

Response to Glkanter's evidence
Glkanter says above ( note: this quote was part of what was clipped when the clerk truncated Glkanter's evidence section to 1000 words ) "In nearly 4 months, it had never been brought to this newby's attention that reliable sources were the vital requirement in Wikipedia". Really? Hmmm. His first edit as a logged in user was Oct 26, 2008. I referred him to the 5 pillars in our very first discussion on the same day and explicitly mentioned reliable sources several days later  and again two days after that. Nearly all of Glkanter's claims are equally specious. -- Rick Block (talk) 19:50, 20 February 2011 (UTC)

Other responses: -- Rick Block (talk) 17:13, 23 February 2011 (UTC)
 * Two sentences are quoted from "Conditional vs. unconditional for the umpteenth time" and presented as if they were individual diffs to the talk page. It's perhaps not obvious that these are simply excerpts from one larger diff
 * About the "overwhelming consensus" - this was Martin's summary of a complex discussion using categories "for change" and "against change" that were not presented as choices in the discussion (i.e. IMO it was a highly biased summary where Martin categorized the opinions, not the editors themselves). My initial response at the time was this (followed up later with ), not the "meow" quote.  The "meow" quote was from several days earlier, subsequent to the following previous direct responses to the same question   (the same question had been asked and answered in a variety of forms numerous times before as well, e.g.    ).  I freely admit this was not civil and that I should not have responded in this way.  Glkanter's response has been to copy and paste this quote into subsequent discussions.

Response to Martin's recently added "ownership" diffs
Martin's quotes are in italics here:
 * Deletes right from the start  The diff here is a talk page diff, where I'm talking about this article diff.  Like it says, the change being reverted here introduces a redundant simple explanation to the lead.  The edit summary points to the talk page.  I'm not sure what Martin is thinking this edit shows.


 * and reverts  Again, a talk page diff. The article diff is, with a summary referring to previous discussion on the talk page.  And, this is not a revert either.  It's an attempt to address the same concern with a (much smaller) change to the article.  Again, no idea what Martin is showing here.


 * argues the maths  - this diff is not a single diff, but a diff between several versions of the talk page. My diff is, which was a response to what was more a less a direct question of me.  In this response, I refer to the Morgan et al. paper (which we had been talking about).  Yet again, I find the point Martin is making here completely elusive.


 * Other editors add their input but Rick edits it all his way  - the context here is this thread (from the same version of the talk page). Martin is presumably thinking this diff is showing I was wp:owning the article content, but if you read the entire thread I suspect you'll come away with an entirely different impression.


 * If only he had heeded his own advice in the last paragraph here  - this is the same as Martin's previous diff. I assume it's meant to be something else.


 * then an anon complains that he is not writing for the average reader  - and the point is what? What I said was "please don't delete it unless you address the Morgan et al criticism in some other way".

Oh, and the Glopk diff shows only that Glopk agreed that this edit was not an improvement. Are you (Martin) suggesting that this was anything more than a good faith, but very clearly misguided edit that was more appropriate to bring up on the talk page? -- Rick Block (talk) 06:01, 22 February 2011 (UTC)

Comment on Woonpton's evidence
I wholeheartedly agree with Woonpton's major point, which is that an important cause of the breakdown here is that reliance on reliable sources has been largely abandoned in preference to how individual editors understand the problem. It's hard to come up with evidence for this, but I'm nearly positive many of the most vociferous folks here haven't read many of the sources (so they don't even know what the sources actually say) and certainly haven't read enough sources to have a broad enough perspective to judge WP:WEIGHT] (perhaps the arbs could poll the participants). The attitude of many editors is essentially "It's a simple problem, I can see that I'm right, and I don't care what the sources say". Richard Gill suffers from this attitude as much as anyone, possibly more so since he actually is an expert on the topic. I have discussed this issue with him off and on (see Woonpton's diffs), and intellectually he clearly understands the point of WP:V and WP:NOR but he still wants the article to reflect his take on the problem (because, well, he's right!). I do not in the least mean to be disparaging Richard's contributions, but everyone here (including him) needs to defer to the sources. -- Rick Block (talk) 21:15, 22 February 2011 (UTC)

Evidence presented by Richard Gill
I'm going to write about content, not conduct. I want to motivate conduct, to give evidence of good faith. To show how collaborative editing of myself with most other editors has led to (potential) improvements in the MHP page which is being blocked by entrenched positions, by polarization.

Much ado about nothing
Would it be a fair bet at odds 2:1 that the car won't be behind the door you first choose?

Would it still be a fair bet at odds 2:1 that the car is not behind the door you first chose (door 1), and knowing the host has opened another (but not knowing which)?

Would it still be a fair bet at odds 2:1 that the car is not behind the door you first chose (door 1), after you saw the host open door 3?

The sensible answer to all these questions is YES.

The reasonings for the first two are so obvious they are hardly worth writing out.

The reasoning for the third YES is just a tiny bit longer. According to many reliable sources in academic probability and statistics, whether it is worth writing out or not is a matter of taste. According to many reliable sources, the following words are enough: by symmetry, it doesn't make a difference which door the host opens, so I would still bet at the same odds.

My position
Rick Block summarized my position thus: the "criticism" that the simple solutions do not address the conditional probability is factually correct, but of little importance since by assuming symmetry the conditional and unconditional answers can be proven to be the same. This is not my opinion at all. Similarly Nijdam seems unable to understand my position.

MHP has been free and open source since Marilyn Vos Savant wrote her words in Parade magazine. There are many ways to interpret her question and many ways to legitimately solve it. It is not the sole possession of some academic community. Simple solutions and conditional solutions are all legitimate, all have their place.

The opposition between the two kinds of solution in the wikipedia artice has been exagerated all out of proportion. The resulting polarization of editors on the page has suppressed other interpretations and other approaches. An editor who offers ways to harmonize the two kinds of solutions is howled down for compromizing a polarized status quo.

To be sure, superficially there is a big difference between elegant popular solutions which give insight into the paradox, and the pedestrian solutions inflicted on mathematics students in Statistics 101. The purpose of the latter is to illustrate the workings of the probability calculus which those students are being taught at the time. Fortunately, the article Bayes theorem already contains the dull standard classroom solution in the context of Statistics 101: as an elementary illustration of Bayes' theorem. No need to repeat those formula manipulations in the article Monty Hall problem. Especially no need, since there are mathematically rigorous ways to solve MHP (conditional sense, or equivalent) which correspond "line by line" to logical steps in short verbal arguments which your grandmother can understand completely. They can be reliably sourced too, and go back to the time of Marilyn's original column.

My publications on MHP promote insights and research of wikipedia editors
The papers I have written on MHP thank fellow editors for what I learnt from the discussions -- a very great deal. They are partly opinion pieces, partly survey papers. The maths is separated from the opinion. The mathematical Truths ("if A then B") are elementary, confirmed by peer review, and attributed to earlier authors. They include some elementary mathematical Truths which other editors (Glopk in particular) refused to allow to be used on the page. It was considered that they constituted "own research" since they did not have "reliable sources" behind them. These were truths at the level of "6 is not prime because it equals 2 times 3". The papers started life as notes written for the purposes of discussion on wikipedia. Later I was invited to recast them as an encyclopeadia article, and from there they developped into a journal publication.

My O.R. rampage
My recent (50, most of them "minor") edits on the MHP page were largely made while drafting a small section with some alternative analyses of MHP which have been compiled from reliable sources, and which show that the difference between the conditional and the simple points of view are actually very small. The ideas and/or the references were discovered by other editors and have been discussed extensively on the talk pages.

Glkanter hammered away with the notion that MHP can be solved by logic, no probability calculus is required. No PhD in maths.

He's absolutely correct and the claim can be backed up with literature references. Modern probability calculus was set up by Laplace in 1814 as a convenient way to package the ordinary logic of "equally likely", based on symmetry, whether coming from physics or from our (lack of) knowledge (indifference). We can go back to basics and do without the formal calculus altogether. It has become a straightjacket. A fantastic tool-box for many purposes, but not the best tool-box for MHP.

And it has been done before!

Symmetry allows one to argue from the outset that specific door numbers are irrelevant, they are independent of the relation between the visible roles of the doors and their hidden roles (hidden to the player, that is). Mathematical proofs based on this logic go all the way back to the time of Vos Savant's article and explain why she herself always denied that MHP had to be solved with conditional probability. Symmetry implies independence and independence implies that conditioning is pointless. Rick Block pointed out the contribution of the statistician William Bell (1982) of the US Census Bureau, who solves MHP (conditional version) in two sentences with symmetry. The very important secondary source Rosenthal (2005) yielded another extremely short proof using Bayes' rule. Richard Gill (talk) 18:19, 20 February 2011 (UTC)

From wikipedia:


 * Editing in an area in which you have professional or academic expertise is not, in itself, a conflict of interest. Using material you yourself have written or published is allowed within reason, but only if it is relevant and conforms to the content policies. Excessive self-citation is strongly discouraged. When in doubt, defer to the community's opinion. In any case, citations should be in the third person and should not place undue emphasis on your work, giving proper due to the work of others, as in a review article. Richard Gill (talk) 15:47, 21 February 2011 (UTC)

Evidence presented by Outside Observer Woonpton
I was surprised when the committee voted to accept the case so quickly, since it looks like a content dispute to me.

Original Research: A Case Study
An important cause of the breakdown on the article, IMO, is that the reliance on reliable sources seems to have been largely abandoned in favor of everyone arguing their own personal elucidation of the problem. This problem isn't limited to one editor, but I will focus on Richard Gill's original research in this section.

Richard Gill is a professor of mathematics who while editing MHP has developed an original synthesis related to the topic; two papers elucidating this synthesis have been published. I am a statistician, and I don't find Dr. Gill's formulation compelling, necessary, or useful for the description and explanation of the Monty Hall problem for the Wikipedia audience. Were I to write a synthesis of the same material, my synthesis would look very different. That's why we use existing secondary independent sources rather than publishing original research.

Richard Gill engages in original research
Gill commented that "the majority of wiki-reliable sources are written by fools" and said that since sources don't say what he wanted to say, he would need to write his own sources
 * OK I have to find reliable sources for all this, and if I fail, I'll have to write one myself.

He defended his developing original synthesis and his idea of Truth:.

He added OR material to the article:

When other editors have tried to make him aware of the necessity for relying on reliable sources rather than original research he has responded rudely, with disdain for Wikipedia policy, one example:
 * ...no matter how brilliantly insightful it may be we simply cannot present an argument that is fundamentally novel
 * I think that the legalistic approach to resolving disputes on wikipedia by invoking OR, NPOV, etc. is disgusting and/or chiildish.)

Richard Gill promotes his own research on Wikipedia
He posted links and notices of his papers to users' talk pages and discussion pages :
 * Those papers do contain the absolutely latest word in comprehensive and unprejudiced mathematical analysis of MHP, offering a sythesis which has never been seen before).
 * It's all written out in Gill (2011) I'm already getting fan-mail from colleagues all over the world for my fresh and refreshing take on MHP...
 * All your problems are solved. As of about today, WP:RS Gill (2011
 * Still no conditionalist has taken the trouble to explain why you *ought* to condition. Only I did, in my recent papers. That is to say: I presented the argument which the conditionalists should have given straight away.
 * I recall people complaining there was no reliable source doing it that way. Well, now there is.
 * At least no stupid editor can now prevent a less stupid editor from using this "Truth" in the future, on the pretext that it is not written up explicitly in some "reliable source".

Also, he was the one who added his papers as sources to the Wikipedia article.

In addition he has hounded other editors about reading his papers:
 * I take it you still haven't read my own work on MHP. There really is no point in talking to one another as long as that state of affairs persists.

response: Gill has argued that I don't understand his British sense of humor, that When I write apparently arrogantly about myself, I know full well what I am doing, it is supposed to be a joke at my own expense. On reflection and on reviewing the diffs again, I don't think the argument undermines the diffs. In each case, the remarks, even allowing for "British" overstatement, convey that his paper has merit, is respected by others in the field,  and should be included in the WP article as a reliable source. In other words, the diffs support the assertion, and the diffs will stand.

Richard Gill belittles other editors
. Even if he's right on the issue, it's not pleasant to be talked down to.

Richard Gill and COI
Gill has repeatedly asserted that as the author of a reliable source, he shouldn't be editing the article, and from December 31 on has pledged several times not to edit the article  But he is still editing the article. Of all contributors, he has the second highest number of total edits, and as of the last edit made on the page as I write this (14:26 Feb 15), 45 of the last 50 edits are his.

Responses
I had responded here to challenges by Gill posted elsewhere, but as the challenges and responses aren't material to considering the evidence, I have removed them.

@Riendog: As I explained here my concern is not so much about Richard Gill publishing research as I am about many editors, including Richard Gill, using the discussion pages to argue their own personal views about the MHP rather than to discuss improvements to the article. The diffs here are just an example of a general problem of the discussion pages being disrupted, even overwhelmed, by arguments over conflicting personal ideas about the MHP (original research).

Experts on Wikipedia
@Martin: I am an expert myself, a PhD-level statistician. I have edited in areas of pseudoscience and fringe science, and have been subject to unpleasant attacks and smear campaigns by those who want to use the encyclopedia to promote scams and schemes. So yes, I am aware of the difficulties experts can experience on Wikipedia (that's why I don't use my own name). But as an expert, I have always followed Wikipedia policy, and I expect other experts to do the same. It appears that Dr. Gill and I would agree on many issues of content, although not on the usefulness of the ideas presented in his papers to the WP article, and not on whether his papers are reliable sources for the article (I would not use Gill, Morgan, or any other primary source.)

On the Monty Hall page, editors are often disparaged for not being experts, for example  where Nijdam says "I don't take any notice of remarks made by glkanter or GerardValentin; they are laymen with no understanding of probability,"and the diffs I supplied above.

@ScW: Experts in a field don't always agree, and experts really don't agree about the Monty Hall problem. If you gave one expert free rein to write the article from his own original research, you'd get that one expert's take on the problem. If you had several experts, each with their own ideas, you'd have...well, you'd have exactly the situation we have now. Which is why we rely on secondary sources instead of individual experts' original research for content.

A short opening note
I wish to note here my sadness that in our evidence we are forced only to denigrate other editors rather that promote ways of working together. I guess I have to work to the rules.

Woonpton's comments
I am very puzzled as to why an editor whom I invited to participate but chose not to should make such a fierce attack on Richard; it is not deserved. Martin Hogbin (talk) 21:51, 16 February 2011 (UTC)

Contributions
Richard has always been completely open about the fact that he is a published author on the MHP. We are fortunate enough to have a interest in this article from an internationally recognised expert on the subject, we should welcome such activity rather than push it away with shouts of COI.

I believe that there is a real danger of WP becoming dominated by 'Google jockeys' at the expense of real knowledge. Many academics left WP in the early days, to the detriment of the encyclopedia. We do not want to drive away those few who are still brave enough to contribute here. This is another case where getting the simple solutions out of the way first would enable editors to cooperate on the following more academic approach to the subject. I am sure that most editors would want to place Richard's contributions to our knowledge of the subject in the article somewhere, I certainly would, and, without the silly argument about the simple solutions, I am sure that we would easily reach a consensus on this matter. Martin Hogbin (talk) 09:08, 17 February 2011 (UTC)

Glkanter
Glkanter, along with myself, has pushed for what might be described as a common sense approach to this article (at least in its first part). Although the essential MHP paradox is a spectacular example of the failure of common sense, our natural intuition concerning the effect of potential host bias is essentially correct. In any reasonable and consistent interpretation of the problem (such as that of Krauss and Wang) the door opened by the host makes no difference. The probability of winning by switching is 2/3. Even the authors of the paper that started the host bias issue (Morgan et al) agree that fact. This fact is intuitively obvious to most people and turns out to be correct. Glkanter and myself have both felt enormous frustration that, after presenting a whole range of rational arguments often supported by experts such a Richard and Boris Tsirelson, other editors have not allowed simplification of (the first part of) the article in the interests of clarity and simplicity for the general reader. Martin Hogbin (talk) 10:12, 17 February 2011 (UTC)

I should add that common sense approach does not mean not supported by reliable sources. Martin Hogbin (talk) 21:46, 21 February 2011 (UTC)

Page ownership
I came here in response to this RfC claiming that no progress could be made because of page ownership by a group of editors.

I trod carefully at first because the article was FA but I do have to conclude that the RfC was correct. A group of editors (Rick Block and Glopk were active at the time of the RfC) have resisted all attempts to make the article more accessible to the general reader. Later on Nijdam joined them and since that time these three editors have exerted a claim to ownership over the article. This hold over the article has prevented many other editors who have tried over a period of over two years from improving it.

My objection is not that they believe that the simple solutions have a weakness, it is that they insist of pushing that weakness in the face of readers right from the start. Any attempt at change that does not do this is quickly suppressed. Most people just do not care about a pedantic detail that makes no difference to the outcome.

Here are, talk page, diffs all from different registered editors who proposed changing changing the page in favour of the simple solutions:

Lambiam gives up in disgust after his contributions are ignored or deleted by the page owners

Father Goose complains that his attempt at showing the simple solutions are always corrupted by the page owners  he then goes on to make the same proposal that I have made several times but to no avail Mathematician Boris Tsirelson agrees with me that the simple solutions are perfectly valid, by symmetry

JeffJor points out to Rick that he is giving undue weight to a few sources and that the article fails to address the needs of many readers

Dicklyon complains about the page owners insisting that the simple solutions always have a disclaimer with them, despite their being published in many reliable sources

Worldrimroamer complains about Rick's muddled OR wording in the article.

Colincbn says that he prefers the simple solutions and points out that the majority of academic sources use them and supports my proposal. 

Melchoir agrees with me that the Morgan solution is not to be specially preferred

Gerhardvalentin agrees with me that the majority of readers are interested in the simple solutions and that the sources do not tell us not to use them. 

Anons from ten nine IP addresses agree with myself and Glkanter as shown on my analysis of the history of the article. Editors agreeing with the page owners are also shown on this page.

Robin Johnson states what he wants from the article and complains that he had to work it out for himself

Here is a quick poll of editors that I tried, to no avail. 

Rick's edits
Deletes right from the start and reverts  argues the maths. Other editors add their input but Rick edits it all his way. If only he had heeded his own advice in the last paragraph here then an anon complains that he is not writing for the average reader. So far I have only reached March 2008.

Glopk's edits
A good tag team player

Replies
I am not suggesting that Rick or any other editor has acted in bad faith just that a group of editors have acted to exert a disproportionate effect on the page content.

Gill110951 is on an O.R. rampage
Since this started, this editor has done way too many edits pushing his interpretation. As an author who publishes on this topic based on what he learned on WP, he shouldn't be closing the loop on his opinions and interpretations this way. He should recuse himself or be topic banned.

As an example, in this diff Nijdam reverts a small part of where Gill has gone way too far, and changed the basic description of the problem from what had been stable in the article for years. A look at most recent 100 edits] shows about 50 in a row to be Gill's, all done days AFTER this case started.

From what I read here, he seems to be more or less on the same side as me. But still, it can't help to do it this way.

Martin Hogbin's position/evidence statement makes the most sense to me
We don't always agree, but in this case I think he has correctly described what the problem is about, and what it should be about. Rick Block and complicators don't seem to be able to accept it. They want the article to be dominated by the recent "academic scholars" whose analysis is really quite peripheral to the problem, and unrelated to the reason it's notable or the reason any would want to read about it. This treatment should get a much more minor weight in the article. Dicklyon (talk) 01:05, 17 February 2011 (UTC)

This is about the same as I said back in 2009. Rick Block is the main stumbling block to achieving a sensible weighting; he is in a minority, but manages to keep tight control of the article, keeping an UNDUE WEIGHT on a minor academic interpretation. Dicklyon (talk) 05:36, 18 February 2011 (UTC)

Nijdam and Rick Block won't let the article move away from their dear "conditional" thing
As Nijdam says in his evidence section, the simple solution "is seriously logically flawed, and it is not acceptable to leave the readers without notifying this." But I don't think anyone is proposing to "leave the readers without notifying this." Rather, the proposals are to deemphasize this interpretation that came from mathematician 10 years after the problem became notable and widely understood. It's perfectly OK for serious mathematicians to find flaws with the way that all the less serious mathematicians get the same answer. But that doesn't mean these serious mathematicians should drive the way the WP article is written, and that's what Nijdam and Rick Block are insisting on, it seems to me.

As an example of how Rick Block works, here's a diff from 4 April 2009; right after I had done a bunch of edit to improve the article in a way that I thought everyone might be able to live with, he simply replaces it all with a new version, with edit summary "improved version from talk page that restores the conditional image among other improvements". That was at 20:24, when the talk page section commenting on his proposed version looked like this; hardly a consensus to take it as an "improved version" and override what other editors were doing.

Nijdam is more blunt. Like here where his summary of his revert is just "you are missing the point". Of course, anyone who prefers a simple explanation is missing his point. More recently, he inserts another whole section to "formalize" the math as he sees it. And here tries to complicate the popular solution by pushing the complexities of his approach into its section. Both of these were reverted, but he keeps it up, always complicating, never allows simple to stay simple.

Some of these editors have behavior problems
As to the behaviors of the various editors, I can see why they misbehave in the face of immovable opponents, but that's really not OK.

For example, even though I was pretty much on his side, Glkanter responds to my good-faith revert of what I took to be a disruptive edit of his this way:, right AFTER the rest of us had agreed to keep it civil. My revert and edit summary that bothered him so much was this diff, after he had inserted multiple copies of "Devlin and many others continue to write articles and text books as reliably sourced references using only the unconditional solution. They make no mention of Morgan or conditionality." in between lines of a proposed actual chronology, including in places where Morgan wasn't involved yet. I don't see how this could have been taken as anything other than incorrect, pointy, and bordering on vandalism, as I said at the time. Then we discussed it for a day or two, relatively civilly, and then he exploded at me. What's up with that? He's still trying to say I was the bad guy there. Anyway, it made me go away, so he won the battle but lost my help on his side of the content disput. Dicklyon (talk) 02:59, 17 February 2011 (UTC)

Here is an earlier good example of Glkanter's style.

As to his comments on this page, I'll just point out that when I reverted him on the talk page, I didn't realize that it was his own creation that he was making pointy disruptive additions to. My revert was in good faith; I admit that I reverted one of his talk page edits; I don't know how my version of events can be seen as a "blatant falsehood". As to the wikidramas that I recount on my talk page, these were not what he characterizes them as; in general, these are about editors who self-destructed without my help, that I happened to be involved with; and a few admissions of mistakes in cases where I edit warred. The problem, as the evidence here and in other sections shows, is that Glkanter has a hard time maintaining civility; certainly a much harder time than I've ever had, even in dramatically stressful situations.

These editors are all inflexible
I tried helping, tried being moderate, finding compromises and middle ground, a few years ago, but after a while realized that nobody on either side was going to tolerate compromise. So I took it off my watch list and let it go, with this goodbye in Dec.09 (the second time I said goodbye, actually).

Rick Block "owns" the article
After a brief but intensive period of involvement in the discussions in March 2008, in which my contribution seemed to be welcomed by Rick Block, I dropped out in total disgust over his method of arguing, which basically amounted to: "Yes, you have a very good point; therefore, let's do it my way". I have not examined the editing behaviour of other involved editors, but it seems clear to me that Rick Block is a large part of the problem. I am not entirely surprised that in the almost three years since, the article has not essentially improved from its miserable state.

Richard Gill is an internationally recognized expert
In any content dispute involving probability I would immediately and without hesitation concede to Richard Gill, as he is a top-notch mathematician and an internationally recognized expert in foundational aspects of probability. --Lambiam 01:09, 17 February 2011 (UTC)

Glkanter's communication skills leave room for improvement
Glkanter's contributions on talk pages are effusive, but it is often hard to see what the point is; sometimes one can only guess. (Diffs seem unnecessary; it is all over the Evidence talk page, including parts moved there from this page.) Unfortunately, when asked to elucidate, Glkanter does not always respond appropriately. This does not contribute to a harmonious editing environment.

There are irreconcilable views on what the content dispute is about
While this arbitration should only be concerned with editor behaviour, it is helpful to understand what the underlying content dispute is about. However, one aspect of the problem is that different editors have incompatible points of view on the essence of the content dispute. In his evidence section below, Nijdam frames the content dispute in a particular way that is irreconcilable with the viewpoints of several other editors. (See also my talk page contribution.) As long as the involved editors cannot even agree what the content dispute is about, there is little hope it can be resolved.

Nijdam lets his version of "truth" trump WP:RS (and thereby WP:V)
It should not be up to an individual editor to decide whether sources are reliable dependent on their notion of truth. But Nijdam considers sources "per definition not reliable" if they happen not to agree with his point of view. (See his subsection Sources below.) --Lambiam 12:03, 28 February 2011 (UTC)

The main difference of opinion
This whole dispute mainly concerns the refusal of in particular Martin Hogbin and Glkanter as active participants to understand or accept that what is called the simple solution, does not solve one important, not to say the most important, version of the MHP, what is called in this discussion "the conditional problem". Being a mathematical fact, Gill agrees, (User_talk:Gill110951), but for some reason wants to promote this simple solution by changing the description of the MHP. Many readers of the article will picture the situation of the MHP as the so called "conditional problem", and will without further notice accept the simple solution to be a correct solution to this version. But it is not, it is seriously logically flawed, and t is not acceptable to leave the readers without notifying this. It is no matter of being overcritical, or desire to be more precise than perhaps necessary.

I have to emphasize that even excellent mathematician, not being well known with probability theory, but even some probabilists, does not understand or let us say recognize this. Nijdam (talk) 09:35, 18 February 2011 (UTC)

In spite of the serious logical error in the simple solution, several sources, although mostly the non-academic, more popular ones, do not recognize this. Also some participants in the discussion do not understand this, and want the article to at least start stating the simple solution a sound solution to conditional problem, and not allow other editors to immediately mention the criticism on it. I suggested a kind of compromise (User_talk:Martin Hogbin, subsection Acceptable formulation, what seemingly has been moved by Hogbin to User_talk:Martin Hogbin,), in introducing a extended formulation of the simple solution, which may be called "simple conditional solution". It is a correct solution (explanation) of the conditional problem. It shows in a more intuitive manner, why the required conditional probability is 2/3. But id didn't lead to the desired consensus.Nijdam (talk) 23:10, 20 February 2011 (UTC)

Glkanter's complaint
As for Glkanter's complaint I should not take notice of his comments, I can say that I discussed fruitless with him for, I guess, more than a year. As it did not lead to any comprehension on his side, nor to any new insight, I stopped reacting. My good right, I think.

Nijdam (talk) 23:10, 20 February 2011 (UTC)

What it's all about here
It's a matter of religion, of ["belief"], not about the "correctness". Just to show the antagonism, steadyly firing of "bad conduct":

The result of the Babylonian confusion of tongues is the Gordian knot. But please notice: "both sides" for years are completely unaware that they are talking about completely different topics, without knowing it. Neither of them is realizing the circumstance. That the heads are looking in two entirely different directions. Using terms that are having entirely different meaning for both. Exasperating. "Babylonian confusion".

And as to Glkanter: Imho there's a difference. If s.o. expresses his "opinion", the way he "feels", and thereafter is said to have "presented a given fact". Imho resulting in a real problem. Gerhardvalentin (talk) 00:43, 18 February 2011 (UTC)

Nijdam
Nijdam is an expert in conditional probability theory. And he is right in saying that, to find the "exact rate of probability" to win by switching (Pws) for "one special game show", a correct mathematical formulation of a theorem should include everything you know up to the time you are giving your answer (in brackets: even if this is not necessary at all to get a reasonable and correct answer). Being an expert in the field of conditional probability, he of course insists in saying that – preceding to answer the famous question "to switch or not to switch? Yes or No?" –  that the exact probability to win by switching for this one special game has indispensably to be determined exclusively by using conditional probability theorems, regarding door# opened. And that this is "the" sine-qua-non condition to be able to give the answer  "yes or no". So the answer not being "yes or no", but the exactly defined rate of probability to win by switching. And so to insist of course on some extensive teaching and training of conditional probability theory to be included within the lemma, and to be the main topic of the lemma on the famous "1/2:1/2" versus "1/3:2/3" paradox. And to firmly insist in using conditional probability theory within the lemma by extensively presenting conditional probability theorems there. As it is written in textbooks for teaching conditional probability theory (MHP is a suitable example for this field to be presented to students). Saying that the correct answer to the famous question can only be the result of applying conditional probability, and proclaiming that any other approach to the answer (yes or no) is incorrect, as it is not the exact result of conditional probability theorem and not answering the "correct" question [].

But repeatedly asked: ''Explain why you *must* use a conditional probability. More importantly, find reliable sources from probability theory which do this'', those questions forever did remain unanswered. .

He is sympathetic, but this is his unalterable and firm "belief". But just not helpful for the lemma to disqualify any other approach. (More or less citing:) To reduce the Monty Hall Paradox to his "only essential and real one MHP", not caring for an overall lucid explanation of all aspects, but rather to push one's favored version. So the partially less lucid state of the article is the result of putting one's version most prominently on the top, and by that creating a "obfuscating" mix of everything".

Conditional probability theory can be very helpful to grasp the paradox, preferably in clear odds-form and easy to understand. That really should be in the lemma. But just as ONE method to help understand the paradox.

The problem is that you can finally understand this attitude, but on the other hand, being no more than just an unchangeable "firm belief", this prevents an improvement of the lemma. Gerhardvalentin (talk) 10:22, 18 February 2011 (UTC)

"What means the MHP in teaching conditional probability theory" versus "what means conditional probability to the MHP"
Important: The WP lemma begins with the famous question: "Is it to your advantage to switch?", immediately followed by the most accepted explicit presumptions, including the principle "that the host must open a door showing a goat, [and] must randomly choose which door to open if both hide goats, and must make the offer to switch."

So, given the formulation of the problem, for the contestant it will be completely irrelevant which door will be opened: Petty and trivial, no difference at all, both are absolutely the same.

And there's no warning there that, in quite differing "host's variants", e.g. given that (though completely unknown) you "exactly knew about the host's very special deviant behavior and special direction" in choosing unevenly, if he has the choice, although he never can change the location of the car, for every game could be giving additional hints on the actual location of the car behind the two still closed doors, so that you "even could know better indeed", if you just "knew" better, in that show. Better knowledge?

The crux is: you know absolutely nothing of all of that, and so even the "most correct" conditional Pws will forever be 2/3. As far to the decision asked.

Quite another issue is, that the "correct Pws" (?) of course can be obtained by maths, including the (irrelevant) "special door" that has been opened. But that's not affecting at all the answer to be given. That's just a matter of the "ability" of maths to "also" deal with the situation, and - maybe even to deal with a special unknown host's behavior, honestly: that just can unserviceably be assumed, with no real effect to a "correct answer".

Btw: That even in the "one million variant", leaving door #777'777 closed – supposed the host just uses to never open this door #777'777, if ever possible, gives you a Pws of at least 1/2 as an absolute minimum, and, considering such approach, vice-versa Pws can also be "1", is known even without needing conditional probability theory theorems.

So the art of conditional probability theory is a topic of its own, but not "needed" to giving the answer asked for.

Of course conditional probability should be shown in the lemma, along with the very modest prominence it has for giving the correct answer. Gerhardvalentin (talk) 02:37, 20 February 2011 (UTC)

Nijdam and Glkanter engage in edit warring
It takes two to tango, and Nijam and Glkanter have engaged in several edit wars. I thought arbcom might appreciate a precise summary of this without tons of content dispute padding.

Glkanter deletes Nijdam's section calling it POV, Nijdam reverts, Glkanter reverts, Nijdam reverts.

Nijdam adds a section, Glkanter deletes it and gives a good explanation as to why. Nijdam reverts and makes a snide comment.

Nijdam deletes a table, Glkanter reverts assuming bad faith on the part of Nijdam, Nijdam reverts, Glkanter reverts.

Please don't chase away Dr. Gill
In my opinion it's absurd to lambaste a professor as a "POV pusher" or a "OR pusher." If you're an expert in your field, then your POV is the scientific consensus and your OR is a reliable and reputable source. It would be a shame to discourage those with the most to contribute to wikipedia from contributing.

Evidence presented by Kiefer.Wolfowitz (uninvolved)
I write to defend Richard Gill from various complaints. I also would urge some writers to withdraw lesser complaints for the common good.

Richard Gill innocent of O.R. rampage
Editor Dicklyon accused Gill of "O.R. rampage", citing primarily the substitution of an inferior passage for Gill's prose. Gill's description is shorter and correct, stating that the "car need not be randomly placed, so long as your first guess is random."

The re-instated version has three errors—an error of factual, an error of scholarship, and an error of grammar: Although not explicitly stated in this version, solutions are almost always based on the additional assumptions that the car is initially equally likely to be behind each door and that the host must open a door showing a goat, must randomly choose which door to open if both hide goats, and must make the offer to switch. Errors:
 * 1) Fact: "the car is initially equally likely to be behind each door".
 * 2) Scholarship: There's no evidence for the "almost always" claim.
 * 3) Grammar: The claim   The phrase "Although not explicitly stated in this version" must modify "assumptions" only through "action at a distance", because the sentence violates Orwell's rule, "put related things together".

I ask Dicklyon kindly to withdraw this complaint.

(Many editors would benefit from reading Orwell's Politics and the English language, I'll add,

as a segue to the next topic ....)

Innocent from "belittling other editors"
In the previously submitted list of diffs, the items seem innocuous:, , , , , , , , . Some were written less to boost the self-esteem of the recipients and more to encourage understanding of probability, by the only method available, study. The royal road to geometry passes through probability only vacuously.

Like Tsirelon, Gill is entitled to view Wikipedians who disagree with him (regardless of whether they are professors somewhere) as students who would benefit from advice. Gill rarely can be irritated with others and he often seems to be enthusiastic about his colleagues' or his own work. However, I don't see Gill making ostentatious displays of effortless superiority or malicious & clever put-downs anywhere: This is a remarkable achievement for a Cambridge graduate!

I ask (outside observer) Woonpton kindley to remove this complaint, as well as the next.

Innocent from COI
Gill thrice declared that he didn't want to edit the article further, because he was concerned about the possible appearance of COI:, , and. Obviously, his declarations were good faith acts, going far beyond WP's COI policy.

He, like any other editor, is entitled to withdraw from self-imposed supererogatory exile from the page, as long as his edits are motivated to benefit the public > the profession > and Wikipedia.

Woonpton needs to rephrase the unfortunate bad-faith allegations against Gill; I wish that Woonpton should view Gill's statements as his declaring a desire for well-deserved WP:Wikibreaks, in good faith. (Perhaps in the future Gill should just declare Wikibreaks rather than announcing cold-turkey retirements from editing MHP.)

Gill has been open about his research, and declared that he has done research on this topic, exemplifying the suggestions of WP's COI policy. He also outed himself for transparency, which is a monumental sign of good faith, imho. Kiefer.Wolfowitz (Discussion) 22:24, 21 February 2011 (UTC)

Closing comment
Editors who are not involved, namely Woonpton and Dicklyon, should consider whether any of their comments are necessary.

I would ask that all editors try to remove all non-essential complaints. Let the good will and good humor of the arbitration committee relax and inspire you! Step back from mutually destructive cycles of accusation and counter-accusation!

However, some of you are unfortunately doomed—doomed to continue editing the Monty Hall problem with one another! "Hell is other people!" Sincerely, Kiefer.Wolfowitz  (Discussion) 02:13, 21 February 2011 (UTC)

Transparency: I've studied one book and some articles by Gill, and I wrote him a short fan-note recently (before I saw this mess). Editor Dicklyon recently commented on my poor grammar, and asked whether I was a foreigner needing assistance! Otherwise, I am not involved with this case, and I've had no discussion with the principals (although Gill has commented on my editing of the WP article on him, today).

Evidence presented by Ningauble (formerly involved)
Disclosure: I am not directly involved in the current dispute except to the extent of my participation in this arbitration, but I did participate (from IP 67.130.129.135, prior to first registering an account) in discussion of MHP for several months in 2008, at which time the analysis of Morgan et al. was first introduced into the article. During that time I interacted with some of the contributors who are party to the current dispute, and expressed editorial opinions on some content issues that are now (still) disputed. ~ Ningauble (talk) 18:11, 24 February 2011 (UTC)

The discussion has a long history of original research
Prior to the introduction of the analysis of Morgan et al., the MHP talk page was primarily used as a forum for discussing the article's subject, e.g. explaining why the naive 50:50 answer is incorrect. (This testimony may be verified by cursory examination of archives prior to February 2008.) This set a pattern of original research and discussion concerning the subject of the article in addition to discussion concerning the article itself. Virtually everyone who has participated in the discussion for any sustained period has at some time posted questions, explanations, or opinions about interpreting or solving the MHP. (This testimony can be substantiated by diffs if challenged, but I am not singling anyone out.) Discussion of the article's subject continues apace in a sub page. Though these discussions have generally been in the spirit constructive inquiry, and have sometimes facilitated article improvement by revealing where the article was unclear, unconvincing, or incomplete, the pervasiveness of original research has resulted in entertaining extensive POV discussion. (This opinion is offered in the spirit of understanding the contributors' dilemma.) Though I may be stating the obvious (it may already have influenced the committee's rapid acceptance of the case), I offer this for the record as context in which irreconcilable dispute arose.

Glkanter renounces civility
Glkanter has repeatedly and expressly renounced civility as "false collegiality," even during the course of this arbitration.

Evidence presented by Joel Michael
I am just someone who was linked this and was curious about it so I wrote a script to test it.

Ruby script empirically demonstrates Monty Hall problem
I made a simple Ruby script which demonstrates the Monty Hall problem in a more empirical fashion. I tried to make it as clear as possible for those unfamiliar with code. The script regularly gives a result of around 66% cars if you switch doors. You can see it here: http://pastie.org/1616283

Evidence presented by officialuser
There is a very easy way of explaining this problem and covering the probablilties.

If you change doors when one is revealed, the only way to lose, is if you picked the right door with your first guess. If you picked the wrong door with your first guess, which happens 2/3 of the time, you will always win in the end.

This should explain it completely.

Evidence presented by Rlendog (uninvlolved up to now)
I am concerned about the assertion by Woonpton (and to some extent Dicklyon) that Richard Gill engages in original research. Wikipedia's WP:NOR policy forbids publishing original research on Wikipedia. But there is no evidence provided that Richard Gill has done that. Rather, he authored papers that were published in reliable sources. As such, referencing those papers does not violate either WP:NOR or WP:RS. While WP:COI notes that "excessive self-citation is strongly discouraged." it also notes that " Using material you yourself have written or published is allowed within reason, but only if it is relevant and conforms to the content policies," and there is no evidence that Richard Gill has not conformed to this. At most there is an issue with pushing other editors to read his paper too strongly. But all but one of the diffs provided on that were directed at one particular party to this case, and that party hasn't suggested an issue in that regard.

As to the article itself, I am concerned that excessive emphasis on the conditional/unconditional issues with the simple solution make the article overly confusing to non-math oriented readers. While this article is about a probability problem, it is a problem that mathematicians barely cared about until it appeared in a popular magazine. As such, and given that it is based on a popular game show, the article needs to be accessible to non-mathematicians. The mathematicians will read beyond the simple solution to learn the technicalities, those not interested in the math issues shouldn't need to.

And in any case, if (given the usual assumptions) the probability of winning from switching is always 2/3 (i.e., the probability of winning from switching is independent of which door the contestant picks and which door Monty Hall opens assuming he has a choice), then the probability of winning from switching given that the contestant opened door 1 is also 2/3 and the probability of winning from switching given that the contestant opened door 1 and that Monty Hall revealed the goat behind door 3 is also 2/3. Rlendog (talk) 20:43, 3 March 2011 (UTC)

The social acceptance of math proofs
Perhaps there's some Wikipedia article covering what I'm writing below in more detail (there's certainly formal research on this), but you should be aware that mathematicians sometimes disagree about how much detail is needed in a proof, especially in textbooks. A well-known example (to me anyway) is the derivation/proof of the reduced/normal form of words/elements of the free group. This is an undergraduate topic, so it's covered in most 1st year algebra textbooks. Some will have very elaborate proofs, some very minimalist ones (i.e. say it's obvious), and some will even discuss the obviousness level in a more or less self-deprecating tone. (Fraleigh & Katz, 2003, p. 341 -- lest someone accuse me of "OR".)

On the article at hand here and its editors
As with anything in Wikipedia, editors taking various entrenched sides in the Monty Hall problem (very seriously, perhaps too much so), both lay and expert, attempt to resolve such a dispute by la[w]yering it with various wikijargon "OR", "NPOV", "RS", "COI", etc. The bottom line is that if proofs have been previously published in reasonable venues, they are acceptable in Wikipedia.

There's always the argument of choosing the orthodox/mainstream proof that is most widely used in textbooks. I'm not enough of a probabilities fiend to tell you if that can even be established here. From the only substantive discussion on this at WP:WPM (here): "I know the problem is of little mathematical interest being essentially trivial. However, as this is one of only 23 Featured Articles about mathematical topics..." Kinda summarizes what this is all about. The consensus achieved at WPM was to "put the more difficult material later in the article".

Update
Ok, what this is essentially about is one WP:RS (Rosenthal) who doesn't edit Wikipedia, but who has fierce advocates here being wrong, and the other WP:RS who does edit here (Gill), and who was even motivated by the others' incomprehension to publish his own writings in peer-reviewed venues, being right. I note that Rosenthal's material appeared in the magazine Math Horizons and in his book, which was probably not peer-reviewed before publication by Joseph Henry Press/Harper Collins (depending on country). Gill published his stuff on this topic in the peer-review journal that he's the head-honcho of (Stat. Neerland.), and in the Springer International Encyclopedia of Statistical Science. And (unpublished in this matter but WP:RS in the general area) Tsirelson (User:Tsirel) also agrees with Gill, for whatever that's worth here.

In the ideal case the ArbCom will pretend they've never decided on content, but still do the right thing. In the realistic case, the ArbCom will [topic] ban a random subset of the people involved depending on their wikilawyering skills. 06:31, 12 March 2011 (UTC)


 * I was president of the Dutch Statistical Society for the last three years or so. The editorial board of Statistica Neerlandica is editoriallly independent of the board of the society. Both boards answer to the annual general meeting of the society. I submitted another paper to Statistica Neerlandica about the same time as my Monty Hall paper. I got a violently aggressive negative referee report and the paper was rejected. I did not complain to the editor-in-chief but I am revising the paper and will submit it to a rather more famous journal. It's true that being a famous scientist might bias one's chances of being published in peer reviewed literature. In this case I think the paper was published because it is good! (As quite a few people told me). And people who are critical of it will be able to publish their criticism: in science we make progress by controversy, by seeking controversy. Richard Gill (talk) 10:32, 13 March 2011 (UTC)

Update 2
Nijdam and Martin Hogbin also have a COI of sorts here, because they wrote a letter to the editor of American Statistician on this:.

Final update
Ok, there are at least four bones of content[-ion]:


 * 1) Failure to admit that what is seen as "canonical" MHP differs between RSes, ergo so does the solution, even if it so happens that several variants have the same optimal strategy.
 * 2) Insistence on a gap in informal proofs of the simplest MHP variant, which broils down to the words "by symmetry". RSes vastly differ in their pedantry about this, and some make their opinion on the pedantry issue itself known to the reader (not unlike the analogy in my opening remarks).
 * 3) Failure to find/use RSes (and which have been out for more than a decade) that frame the problem in game theory terms as one of finding an optimal strategy, rather than prob/stat 101 "calculate the conditional probability...", which make the fist two issues slightly more clear. (For example, the player's strategy has two bits/booleans: [switch if Monty opens door 2, switch if Monty opens door 3]. If Monty has an asymmetrical strategy/preference for opening a door when he has a choice, then the answer to these questions could potentially be different, so a bit more work is needed to prove that the optimal strategy is to always switch.)
 * 4) Failure to frame/address (and quite possibly for some editors even comprehend) issues with interpretation of probability that some RSes discuss in relation to MHP. (roughly: is what we're told just happened the complete set of rules of the game, or could we be making a faulty generalization?). This generates even more MHP variants, also covered in some RSes giving more fights to pick over "what vos Savant really meant"; quality RSes separate the math on solving clearly stated problems from their opinion on this kind of issue, if they even venture it at all.

So, you have at least four issues on which any two long-term editors of this article can and do disagree with high probability. When I wrote the failure or insistence bit for every issue above, I gave you my recently formed POV. You can randomly flip some of the bits and obtain someone else's opinion.

The behavioral issue here, if one can even be distinguished from how Wikipedia normally works in any remotely controversial area, is that a number of editors meet edits flipping their most beloved bit(s), or even mellowing them a little, as "proposing major changes without consensus!" 07:51, 15 March 2011 (UTC)

Not embracing Wikipedia Policies and Guidelines
Over time I have become a true believer in Wikipedia Policies and Guidelines. I had my doubts at first, but I have found, again and again, that embracing the policies solves many problems. You can read my thoughts on how I believe that embracing Wikipedia Policies and Guidelines will help in this case on the talk page. Consider, if you will the very first notice on the page you are reading: "Create your own section to provide evidence in, and do not edit anyone else's section" (emphasis in original). And yet, when I read the above section above, written by Tijfo098, I see that Glkanter has edited it, despite the clear notice and despite his previous run-in with the 1000-word rule. If he is unable / unwilling to follow the rules here, where his behavior is scrutinized by an arbitration committee deciding who to sanction, it is unlikely that he will follow the rules when he is out of the spotlight.Guy Macon (talk) 09:23, 12 March 2011 (UTC)


 * UPDATE: Glkanter deleted the edit two minutes after I posted the above, but it is still in the history. Guy Macon (talk) 11:29, 12 March 2011 (UTC)

Evidence presented by {your user name}
before using the last evidence template, please make a copy for the next person

{Write your assertion here}
Place argument and diffs which support your assertion; for example, your first assertion might be "So-and-so engages in edit warring", which should be the title of this section. Here you would show specific edits to specific articles which show So-and-so engaging in edit warring.

{Write your assertion here}
Place argument and diffs which support the second assertion; for example, your second assertion might be "So-and-so makes personal attacks", which should be the title of this section. Here you would show specific edits where So-and-so made personal attacks.