The article was removed by Dana boomer 14:51, 13 June 2011 [1].
WP:WIAFA concerns (1a, 1b, 1c, 1d, possibly 1e, 2a) are detailed below. But before delving into the details, I'll point out that there are major, long-term disagreements among a number of editors on how to present the topic involving the tension between WP:MTAA and WP:NPOV that have been going on for years, and culminated in an ArbCom case where two of the long-term contributors have been sanctioned, and several placed on restrictions or reprimanded. Unfortunately, the departure a couple of ArbCom-sanctioned editors has changed nothing of substance in topics in disagreement between the remaining editors. The issue that WP:FAR should be concerned with is that those disagreements have negatively impacted the end product: the article itself. Below, I organize my presentation by topic rather than WIAFA criteria, because some topics involve multiple criteria (even butting heads depending how one chooses to favor clarity or their view of npov) but I'll point them out. Before continuing, I disclose that I have contributed a couple of large-block-size diffs to this article, and a few minor ones. Of course, whether a change is semantically major or not doesn't exclusively depend on how much text is changed, so below I review the revision of the article before I had contributed anything, particularly because several long-term contributors to this article think that some of my edits were not an improvement.
1) Lead clarity vs. npov issues on the multiple interpretations/variants of the natural language statement leading to distinct mathematical problems. (WIAFA 1a, 2a, and 1d) Can you tell what do the words "randomly" and "overall" mean in the following chunk of the lead (emphasis mine)?
“ | Although not explicitly stated in this version, solutions are often 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.
As the player cannot be certain which of the two remaining unopened doors is the winning door, and initially all doors were equally likely, most people assume that each of two remaining closed doors has an equal probability and conclude that switching does not matter; hence the usual answer is "stay with your original door". However the player should switch—doing so doubles the overall probability of winning the car from 1/3 to 2/3. |
” |
The part of the lead quoted I have quoted is supposed to communicate a mathematical result, as opposed to the vos Savant version just above it. Can you tell if the emphasized words are there for a purpose or are superfluous? What is hidden behind those two is the mathematical equivalent of WP:WEASEL wording that is trying hide a dispute in the interpretation of vos Savant's words, as I tried to explain [2]
“ | Although not explicitly stated in this version, solutions are often 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
uniformly choose which door to open if both hide goats, and must make the offer to switch. As the player cannot be certain which of the two remaining unopened doors is the winning door, and initially all doors were equally likely, most people assume that each of two remaining closed doors has an equal probability and conclude that switching does not matter; hence the usual answer is "stay with your original door". However the player should switch—doing so doubles the probability of winning the car from 1/3 to 2/3.
A common variant of the problem, assumed by several academic authors as the canonical problem, does not make the simplifying assumption that host must uniformly choose the door to open, but instead that he uses some other strategy. The confusion as to which formalization is authoritative has led to considerable acrimony, particularly because this variant makes proofs more involved without altering the optimality of the always-switch strategy for the player. In this variant, the player can have different probabilities of winning depending on the observed choice of the host, but in any case the probability of winning by switching is at least 1/2 (and can be as high as 1), while the overall probability of winning by switching is still exactly 2/3. |
” |
Rick Block writes that the distinction between the two interpretations (and thus two mathematical problem-objects, one a subset, i.e. particular case of the other) is not important enough for the lead. It may not be immediately apparent why this is also a WIAFA 2a issue, but it becomes evident once you try to read the rest of article: the lead simply fails to prepare the reader for the problem variations which the proponents of various methods argue that their method is "the best". David Hilbert said "He who seeks for methods without having a definite problem in mind seeks for the most part in vain." The major problem variants don't have to be in the lead, but they should be certainly be stated before the several solutions are given, because these also try to convince the reader that the other approaches are wrong or superfluous.
There are plenty of secondary sources that make this separation, e.g. Rosenhouse (2009) ISBN 0195367898 by chapter, but not Wikipedia. In a similar vein, User:Kmhkmh argues that even presenting one of the variants ahead of the other is "nothing but a subtle POV pushing". If you wonder how this could possibly be so, the answer is the next paragraph.
2) Another lead issue is that MHP made it to the pages of the New York Times (the first time around) in no small part because mathematicians disagreed on what math problem vos Savant's words should translate to, with some of them proposing even other variants besides the above two. Of course, I'm not proposing a list in the lead, but a large part of MHP's notability is due to its confusing language, at least in its original formulation, which should be said in the lead (WIAFA 2a/1d).
3) Using a degenerate case to illustrate the use of the "best" proof method for a more general problem/variant. (Like insisting on solving using the quadratic formula). I argue that doing this is confusing for the reader (WIAFA 1a) and I gave a list of RSes not doing this (besides Rosenhouse), i.e. who explicitly introduce the general case or a particular non-uniform (usually deterministic) strategy for Monte, (e.g. always showing preference for one of the doors when he has a choice) before using a general method. Rick Block however says that doing so in not npov (WIAFA 1d trumping 1a), arguing that the majority of math sources do this. Even assuming this is true (a claim for which he provided no evidence), it's still not clear that a head count is the best selection criteria for proofs. I tried to engage him in a more detailed discussion on how he compares two proofs for authority by asking him to compare one from Ken Binmore with one (Morgan's) Rick seems to favor, but so far without getting any reply on that.
(I'll stop with giving WIAFA callouts from here on because they are obvious for the remainder of this review.)
4) Inconsistent terminology throughout the article. Examples include referring to overall/average probability but also calling the case/path probability total. Requests to synchronize terminology from different sources met with "I'd rather not change it". As a results, the article is a terminological pastiche, contravening WP:MOSMATH.
5) Disorganized presentation and tangentiality. Before and after giving some solutions with quote/paraphrases whether the "simple" solutions are wrong, without ever trying to present this matter coherently (because that would require explicitly stating several problem variants). Text reads like "blah, blah, blah, did I mention the simple solutions are wrong?, blah, blah, ... , did I mention the simple solutions are wrong?, blah, blah, ..., did I mention the simple solutions are wrong?, blah ..."
6) The above is the result of endless POV wars between true believers in the various solutions, who frankly seem to be clueless that are talking about different problems. ArbCom didn't ban all of them, unfortunately, only the worst offenders. The counterpoint to the oft repeated (from one source!) claim that simple solutions are wrong, i.e. "the simple solution is right in the case of equal conditional probabilities (because the overall probab. is their average)" has been recently deleted from the article as "unverifiable" even though it was cited. Quite amusing chutzpah, given that several other sources concur with that, e.g. Rosenthal 2005/2008 [3] and those are free on-line. Ironically Rosenhouse cites Wikipeida for inspiration when making this point at p. 52 in his book. I guess this makes him completely unreliable per WP:CIRCULAR! He read the WP:Wrong version too! Someone email Science (journal) (which published a reviewed of the book doi: 10.1126/science.1177947) right away! Never mind he is a math prof at James Madison University, and can probably evaluate whether a argument like this is convincing or not.
7) The problem variants from given the large table are poorly organized and some are of questionable relevance. Never mind they repeat the snuck-through-the-back door variant that this-or-that solution was really solving. E.g. "The host acts as noted in the specific version of the problem." I have no idea what that refers to. Or "The host opens a door and makes the offer to switch 100% of the time if the contestant initially picked the car, and 50% the time if she didn't. Switching wins 1/2 the time at the Nash equilibrium." If you assume that the host strategy is fixed, it's a little silly to speak of a Nash equilibrium. It's a one-player game against nature, something that many game theory books don't even consider a game. Some decent secondary source like Chun 1999 or Rosenhouse should be used to organize variants.
8) Excessive formulism (for lack of a better term) is one of the Bayes' solution #1. Self-evident eye sore.
9) The "Sources of confusion" section is confusing if not downright POV. There are two issues: people being confused after being presented a definite math problem, and people being confused by the ambiguous formulation(s). No attempt is made to separate these. The implicit assumption there is that those making different assumptions about the game are idiots (other than Morgan of course, we are again reminded that the simple solutions are wrong!), including the profs from the NYT piece, and sources like Chun 1999.
10) Poorly researched from a formal sciences perspective (i.e. limited to STAT 101). Trivial variations between a bunch of proofs are presented as something of note. My note on the lack of serious game theory treatment in the article, which (I think) stymies understanding and only prolongs the absurd discussions, have been met with repetitions of the same obsessive "unconditional vs. conditional" mantras which have nothing to do with this issue. As David Eppstein put in on the ArbCom page, the so-called "advanced solution" using Bayes' theorem is the "basic of basics" as far as probability & decision theory is concerned.
Bayes' theorem vs is like mom's meat grinder next to a food processing plant when up against extensive-form games and Markov decision processes, (no need to skin the pig or chop the meat manually before the machinery takes over). As Ken Binmore puts it, once you formulate it as an EFG you hardly have to (creatively) think at all, meaning you just apply a well known algorithm to solve it. (Same goes for MDP or formulating it as a Bayesian game). Sources usable for this:
The fact that the above two are equivalent approaches is non-trivial in general, a result that played no small part in these guys getting a Nobel prize.
10) Issues related to interpretation of probability not discussed. Suggested source: Georgii ISBN 3110191458 (3rd ed.) pp. 54-56 (More correctly these are framed as issues stemming from what can or cannot be assumed common knowledge (logic). Crucially, the definition of a game like EFG assumes the rules are known by all player.) Also Rosenhouse pp. 84-88, but it's less useful. Olofsson ISBN 0470040017 pp. 50-52 discusses it the same way as Georgii, but with less formalism.
11) Issues stemming from bounded rationality not discussed. E.g., doi: 10.1002/bdm.451 Related to this, Rosenhouse p. 135-136 discusses "feeling bad about switching" (Olofsson also mentions this), and with Chun 1999 codifies this as an alternate game where the Von Neumann–Morgenstern utility does not equal the lottery probability. Chugh and Bazerman 2007 [5] is a good overview here.
12) For the uniform problem a combinatorial argument (with 6 layouts by numbering the goats) is given in Rosenhouse p. 54 (taken from Williams ISBN 052100618X pp. 73-74). Richard Isaac discusses a slightly different sample space counting approach in ISBN 038794415X, pp. 8-10. These are sufficiently different proofs to include I think. (Isaac also discusses the Gillman, OMG subtle POV variant, if you're curious, on p. 27)
I hope some article improvements come out of the above, but I'm not holding my breath. A fair number of editors repeat on talk the article is fine. Others make weird edits with strange if not misleading summaries reminiscent of WP:ARBPIA articles and stonewall to perfection on talk. Of course, this article may well deserve its FA star as "the best Wikipedia could ever produce on this topic given its social dynamics", but the answer to the question: "is this article a good presentation of the topic based on the sources available", the answer is clearly no in my mind. Overall the article reads to me like it was produced by a committee of humanities journalists who read a few math articles, and cobbled them together without really understanding what they are saying or trying to integrate them in a coherent (mathematical) presentation.
And as a courtesy for my time investment, please do not edit what I wrote above to either strike anything or interject your replies between my paragraphs. I have numbered the issues, so you can easily address them in the unlimited space below, and let the FA(R) director/delegates decide. Tijfo098 ([[User talk: |talk]]) 23:23, 7 April 2011 (UTC) reply
@Tijfo098: Since I'm incorrectly cited above, I'd correct that and clear up some possible misunderstandings as well.
-- Kmhkmh ( talk) 03:24, 8 April 2011 (UTC) reply
FWIW, I prefer less technical approach in the lead; for example, I had no trouble understanding "chooses randomly" (Donald O. Granberg's review in Science of Rosenhouse's book uses the same word in its own lead paragraph). "Uniformly" (while more precise) is IMO likelier to confuse a non-mathematical reader. In the arb case discussions I mostly agreed with Glkanter's content preferences, and found it sad that he was so terrible at collaborative editing that he had to be banned (there was really no choice about that).
That Granberg (the book reviewer) is a sociologist rather than a mathematician gives me the idea of trying to "user test" the article, by going over to a non-mathematical wikiproject (like sociology) and asking for volunteers to read various versions of the articles and say which parts they found understandable. As math nerds we all understand the subject too well to put ourselves in the heads of the non-math people we are trying to communicate it to. 69.111.194.167 ( talk) 08:34, 21 April 2011 (UTC) reply
Comment This article has been at FARC for over two weeks, with little discussion in this section. Could we please get some comments on whether the interested editors believe this article should be kept or delisted, or whether additional work is needed and ongoing? Thanks, Dana boomer ( talk) 14:36, 10 May 2011 (UTC) reply
Delist. After months of working out a plan to resolve the longstanding content dispute that resulted in an arbcom decision and major changes to the article that pretty much everyone agrees made it worse than it was when it was made an FA, I have pretty much given up (I did ask to be notified if some day they are ready to try my proposed solution.) I can no longer advocate keeping this a FA in its present state, and I no longer believe that any real progress is being made toward resolving the issues. The individual editors are doing av good job, but they are working at cross purposes because of the longstanding content dispute. Guy Macon ( talk) 19:18, 1 June 2011 (UTC) reply
User behavior is still fine - no edit wars, no personal attacks, etc. Following Wikipedia policy is also good - everybody is citing reliable sources, no original research, etc. What has deteriorated is the chances of resolving the basic problem of different statistics professors being fairly evenly divided between two quite different and incompatible ways of explaining the Monty hall problem, with each group insisting that their way of explaining it must be in the lead and the other way of explaining it not be in the lead. I had come up with a plan which involved getting both sides to agree on creating two versions in talkspace that differ only where the content dispute required. Then I planned on shepherding the dispute through content dispute resolution and attaining consensus among a wider group of editors (nobody wants to wade though page after page of talkpage arguments about statistics) Alas, one of the most vocal proponents of one of the two sides refuses to cooperate with my plan. There is no requirement that he cooperate, of course, but without everyone agreeing on an easy to understand document showing exactly how the two sides of this highly technical mathematical dispute will look when translated to a Wikipedia article, I just don't see how I can expect any editors who don't happen to be statistics experts can judge the two sides of the dispute properly. So we are left with a good-faith content dispute, with both sides having quite reasonable - but highly technical - arguments as to why their POV should prevail. All efforts at compromise have failed. The arbcom action was a huge success at fixing the misbehavior issues, but of course the arbcom does not rule on content disputes.
Perhaps someone else might want to take a shot at being a neutral voice that does not take sides in the content dispute. I am getting a bit burnt out and am taking a break from it. Guy Macon ( talk) 14:37, 2 June 2011 (UTC) reply