User:I JethroBT/MontyHall

Prior relevant discussion

 * RfC to-be-closed
 * Mathematical arguments regarding various problem solutions
 * April 2012 ARBCOM ruling
 * Mediation Cabal discussion
 * |Archived 2011 Request for Mediation discussion

Comments from

 * Possibly splitting the article so that the simple solution is in an article with the common name and the complex solution is in another article would be a good solution??
 * The simple problem is pub level mathematics, the complex problem is cutting edge mathematical research?? and certainly bayesian statistics is at a much higher level, combining both of those is hard.
 * My general experience of Wikipedia's maths articles is that articles are at the level of ones current understanding - with the more specific ones being at a higher level of required mathematics.
 * This meets WP:TECHNICAL.
 * The RFC comments seem to lean towards proposal 1.
 * Certainly the RFC comments lean towards primarily covering the simple solution - with some detail on the more complex solution.
 * The lead does seem to be rather long and should be shrunk - possibly not mentioning any solutions in the lead is sensible.
 * However covering a solution seems reasonable as per MOS:LEAD.
 * Certainly saying that it is better to switch should be covered in the lead.
 * Calling the simple solutions "simple" seems to be problematic - there seems to be a consensus against doing that.
 * Obviously the host knows where the car is, if that isn't a requirement then it is a different problem.
 * Derivative is a good example. Most of the content is first year university or lower at least until the vector/PDE stuff.

Comments from
(Note to other editors: These are not my final opinions, as I have not been able to fully incorporate the entire RfC into my observations below.  They are subject to change at any time during this process.)

Neither

 * Many editors supported neither proposal because they are concerned that either proposal would suffer from the same content-disputes in the long-run. There were a number of reasons editors supported that notion:
 * Neither proposal recognizes the disparity in the titles of the approaches. One is called a "simple" solution, whereas the other is called a "conditional" solution.  The fact that the former is called simple is problematic in that it might be construed as less correct, and would be subject to further criticism.
 * Neither proposal supports language changes to describing what these solutions really are, which are approaches in the opinion of one editor. They can be solutions given that the problem is contextualized in a particular way.
 * Related to the above point, neither proposal achieves showing readers the problem from an angle they are unaccustomed to.
 * Neither proposal sufficiently addresses giving due weight, but proposal 2 is more problematic in this regard.


 * Most editors seem to agree with the proposals in that the simple solution should be presented first, followed by the conditional solution. An editor also expressed that these solutions should be presented practically last in the article, preceded by history and simulation findings.
 * The lead should not provide any solution or approach, as this could cause the dispute to persist.
 * An editor expressed the idea that conditional solutions rely on an esoteric understanding of probability that is rarely discussed in MHP lit. As such, creating a conflict between this and other solutions should not even be happening at all.
 * But, there are clearly many sources that express reservations about the simple solution.


 * There is a failure to contextualize a lot of the criticism about vos Savant's solution, e.g.:
 * Critics have noted her solution is actually correct in some conditions, but only doesn't account for variants in host's behavior.
 * The standard problem specifies a kind of selection (uniformly random) that does not disqualify vos Savant's solution and resolves issues of strategy.
 * Some sources state that the vos Savant solution cannot account for host variant behaviors, but do not state that it is incorrect.


 * An editor said to basically leave it as is because it 1) starts with simple concepts and readers can move on as needed and 2) The article doesn't seem to test the WP:OR or WP:POV waters very much as there is an clear section challenging the veracity of the original solution which is supported by reliable sources.

Proposal 1

 * Simple solutions represents a bulk of the coverage of the material here, according to some editors (verify this), and so should be proportionally represented in the article per WP:WEIGHT.
 * Simple should also be shown first and ought to be the most prominent because it is what readers are looking for. (WP:ASTONISH)
 * The article should generally focus on common assumptions (i.e. random choices from host and the contestant is given a choice) and then followed by the "strange" variant. The purpose of the article is not to unravel the problem, but to make the structure clear to readers.  This proposal will accomplish that, the editor believes.
 * This structure:
 * Better captures the spirit of the problem (according to whom?)
 * Better reflects the standard problem (OK).
 * Is ideal, as Wikipedia is not intended to be mathematically rigorous. (Well put).

Proposal 2

 * An editor expressed concern that many sources that present the simple solution are popular, not academic.
 * However, "popular" does not necessarily mean unreliable.


 * According to WP:NPOV, because there are several commentaries criticizing the simple solution published in academic journals, they ought to be represented by way of this proposal. Proposal 1 suggests that the simple solution is "the answer" and is not disputed.
 * Proposal 2 is ideal because while both simple and conditional solution reach the same answer in many cases (2/3), they differ in their approach. In addition, the math is "incorrect."
 * An editor stated that all opinions that don't truly understand the premises of the problem should be disregarded.
 * Personally, I did not see any strong evidence that any participants (save for one who struck their comments) in this RfC failed to understand the content issue or the problem parameters.


 * One editor believes that readers are more likely to look for a more rigorous solution
 * This seems awfully speculative and also unlikely. It is also against policy per WP:UPFRONT.


 * The unconditional solutions take liberties with the problem parameters; readers will sense something is off with simple solutions.
 * Again, I don't think there's any strong evidence for this claim. There is a uniform, standard problem with random choices.  Furthermore, while there has been dissent among a significant minority about "something being off," there has not been much dissent from the average editor.  I, Jethrobot  drop me a line (note: not a bot!) 03:28, 14 October 2012 (UTC)

Statement of contentions
The issues with the Monty Hall problem article (which I humorously call Monty Hall problem's problems) are that many editors disagree on the following matters:
 * Whether simpler approaches (or solutions) such as vos Savant's and conditional types should be distinguished as "incorrect" and "correct" respectively.
 * Whether one solution should be given more prominence than the other, in terms of:
 * Description in the lead
 * A criticism section on simpler solutions
 * To a lesser extent, how the approaches should be described in the layout of the article itself.


 * Whether more or less weight should be given to the criticisms of simpler solutions, and whether those criticisms should be contextualized.

What ideas relevant to the proposals have some consensus?

 * The article should start with simpler ideas regarding the problem and build up to more complex ones. Specifically, vos Savant's solution should be described first (wherever that may be) before the conditional solution. (Supported by WP:UPFRONT, WP:ASTONISH).
 * There is a preponderance of coverage of simpler, non-conditional solutions that do not account for host knowledge or behaviors.
 * Many editors agreed with neither proposal. This because was neither proposal sufficiently addresses WP:POV and WP:WEIGHT issues the proposal was intended to rectify for a variety of reasons.  This failure, in the opinion of some editors, will prolong content disputes.  As Ninguable put it, both proposals give too much weight to the debate itself.
 * Many editors did not support the addition of a criticism section. Some editors felt this would prolong content disputes, rather than settle them.

Policies

 * WP:NPOV
 * WP:WEIGHT - Wikipedia should not present a dispute as if a view held by a small minority deserved as much attention overall as the majority view. In the spirit of this idea, it also should not present a dispute with undue weight if that dispute stems from a minority.
 * WP:IMPARTIAL - Wikipedia describes disputes, but it does not endorse or reject sides; the purpose of the article is not to solve the problem for readers, but to describe it and its solutions proportional to their coverage.


 * WP:OWN - At least some editors claimed that many opinions in this RfC should be outright disregarded because, in their opinion, they did not understand the problem.

Guidelines

 * WP:MTAA
 * WP:UPFRONT - It is completely legit for an article to have very technical content, but it must come later. Initial content should be the most accessible for readers.
 * WP:EXPLAINLEAD - The lead needs to be as broad as possible to be accessible to readers of a variety of educational backgrounds. It is less important for it to as qualified as possible when it comes to making distinctions on the "correctness" of different solutions.


 * WP:LEAD
 * WP:MOSINTRO - The lead section should briefly summarize the most important points covered in an article... Jargon must generally be avoided, and when needed, they must be put in context.  Readers need to be eased into the content.



Essays

 * WP:BETTER
 * WP:ASTONISH - If the lead is going to present a solution, it really shouldn't overwhelm readers with the technicalities of how one, according to some researchers, may not be correct.


 * WP:AESA
 * Realize that different approaches or explanatory models are often all correct, and different readers will find different explanations useful.
 * Assuming that you are right gets in the way of engaging collaboratively at the talk page. Claims of personal expertise are generally useless here also, since we will not be verifying your identity.

The issue
The problem statement: The Monty Hall problem, going back to the 1950s (in academia) came to public notice (and WP notability) by Marilyn vos Savant's publication in the for-the-common-person magazine, Parade. She also provided a simple solution: per her there were two things happening in the problem, a person choosing a door, and then either sticking to the choice or switching. That would be two combinations in all. The first combination, choosing a door and sticking to the choice, had a chance of being right of 1/3. Since the other combination was the only alternative, its chance of being right was 2/3. Some academics have questioned whether her formulation is rigorously accurate and whether it can be generalized. There are other solutions of the same caliber: one from Krauss and Wang (a figure showing all possibilities and showing for two cases it is better to switch and for one, not); one from Carlton; one from Adams/Devlin; and one I will call the multi-door perspective. The rigorous proof uses conditional probabilities and hence the notations of probability theory. Should we present the simpler imprecise solutions first (either in the lead or in an introductory section) and go to the precise version next, or do it the other way around?

Debate summary

 * Proposition 2 hinges on accuracy concerns with the simpler solutions. Several sources have been cited by an editor to buttress the claim academia "disagrees" with the solution. Per this editor, some academic sources call the solution plain wrong. The editor implies the proposition 1 solution cannot be included first without breaking WP:UNDUE and WP:NPOV, the neutral view being giving more weight to what academia considers more accurate. The vote count favors proposition 1. Many of those who favor changing the article beyond these propositions (and hence beyond the scope of this RFC and our summation) also say they oppose proposition 2 more than proposition 1. In rebuttal, editors mention Wikipedia consensus is not assessed by votes alone, though they do play a part. One editor mentions mathematical truths are not decided by votes at all.


 * Proposition 1's backers state an accessible, even if not rigorous, solution should be first presented, before presenting the ones which meet the standards of math rigor. They state historically the problem came to public light in a non-mathematical context. An editor has rebutted the objection to proposition 1, stating the academic objections are to 1. Von Savant's wording of the solution being interpretable as an unconditional probability problem, and hence not a direct solution to the proposed problem, and 2. Von Savant's solution (and other proposed simple solutions) not being generalizable to variants of the problem. These are not concerns for Wikipedia.

Policies and guidelines

 * Policies: WP:V, WP:NPOV, WP:OR
 * Guidelines:WP:RS, WP:MOSINTRO, WP:LEAD, WP:UNDUE, WP:JARGON, WP:MTAA, WP:RFC

Analysis

 * Analysis of weight of arguments for the lead: The relevant guideline is WP:LEAD. The lead is both an introduction and a summary of the important aspects of the body text. The length of the summary is governed by WP:LEADLENGTH and should typically be 3 to 4 paragraphs long. We cannot include proposition 1 in the lead and proposition 2 in the text or the other way around. What should be in the lead directly reflects what should be in the text, and hence no separate analysis is needed here. The order of props 1 and 2 should follow that in the text, and the summary of prop 2 should have no equations or formulas per the WP:MOSINTRO referred to by editors in the discussion. Yes, these are guidelines and not policies and can be broken if editors agree that is best, but clearly editors do not agree. In such a situation, sticking closely to the guidelines is warranted.
 * Analysis of weight of arguments for the body text Of the three simple models of proposition 1, I note no objections to the Carlton solution (a distilled version of the vos Savant one) or the third simple model: that of considering all the Monty-opened doors and the switched-to door as one big whole. Perhaps that may be from the format of the discussion, limiting the words, but I don’t find any criticism in the article either. All the references there object to just the vos Savant simple solution.


 * As to the vos Savant simple solution, were I to paraphrase the support for proposition 1. the following way, not adding anything of my own except for what is in footnotes, which way the evidence leans becomes clearer. She gives the right answer for three doors with Monty opening one randomly without a car in it. That the version is imprecise is an issue for a math journal, but not for a general-purpose encyclopedia. That the version is not generalizable to certain cases is an issue for math teachers and researchers, but not to the general public. That her version is inaccurate depends on how accuracy is defined—the results are clearly accurate. The gaps in her wording are the gaps of normal written language which depend on readers assuming a specific context and specific sequences of standard actions. The Rosenthal objection is that the result does not generalize to Monty Fall and Monty Crawl. What the Lucas paper means by "incomplete" is that vos Savant’s logic doesn’t work for variants. Eisenhauer just quotes Morgan.

My take on the objections
I don’t think mathematicians are the best judges of what a model phrased in common English means. The other objection of not enough precision is, generally speaking, what one should expect from a layperson summary in English, not using the precise notations of math. The final objection, that the result is not generalizable, is not relevant to a summary meant for the layperson; it applies to summaries meant for students of mathematics, the targets of at least two of the journals sourcing the objections (see "local footnotes"). We are required by guidelines to provide the most-accessible version of a proof if it is correct, even if it is not generalizable and precise enough to be used by math students and the authors who publish in journals for them. Churn and change (talk) 02:49, 12 October 2012 (UTC)

Summary
In both text and lead the simpler propositions should be presented first, and the formal solutions later at the same heading level. The best order, in my opinion, is Krauss & Wang, vos Savant, Carlton, Adams/Devlin and the multi-door point of view. Whether objections to the simpler solution merit a mention in the lead depends on analyzing the citations supporting them (I have provided some basic facts in the footnotes, but a conclusion is beyond the scope of this RFC since this issue was not discussed, though mentioned early). How much compression happens from body text to lead is specified by WP:LEADLENGTH. Whatever restructuring and cleaning up the article needs (I see the vos Savant 1990 citation in the lead links to nothing) can be done after this part is settled. One suggestion there would be to move the mathematically rigorous wording of the problem and the section with complaints about Savant's wording somewhere way past the very beginning of the article; they interest largely mathematicians.

Local footnotes
References containing objections to von Savant's solution (note most are meant for undergrad math majors and hence are concerned about generalizability of this solution's logic):


 * Morgan: Author from Old Dominion University, New York. Publication per has impact factor 0.96, ranked  25th or so according to Comparison of statistics journals.


 * Rosenthal: Author from University of Ontario, publication MathHorizons is for undergraduates interested in math.
 * Gillman: Retired UT Austin prof. Publication American Mathematical Monthly  has impact factor of 0.34 (too low to bother with ranking)


 * Lucas: James Madison University. Mathematics Magazine: expository journal of undergraduate mathematics.


 * Eisenhauer: Canisius College, New York. Teaching Statistics (not a research journal, so no impact factor).

Start of discussion
Draft complete enough to start discussion:

Churn and change: Yes

I Jethrobot: Yup!

Eraserhead1: Sure, I don't think I need to go into quite as much detail as you guys - your thoughts are basically the same as mine :).

I think we pretty much agree overall on the core question of the RFC itself—which of the two solution-groups should come first. Also to best not call first group "simple solutions." Objections to vos Savant's solution are to its generalizability and perhaps lack of math rigor. (I note the objections are included in journals meant for math teachers and undergrad students; for them how well the solution generalizes, and what math can be learned from it, matter more). Solution-group 1 is accurate enough for it to be considered first. There is no need to add words such as "random" and "uniform" since the common understanding would be Monty just arbitrarily picks a door without a car in it. We need to go with our own understanding of what a layperson finds easier to read, instead of depending on some one-off psychological study (somebody has quoted some psych. paper).

A quick summary of some areas where we could reach consensus on details:


 * I think the lead is a non-issue; it should reflect the body text, and not have something new. So we can't have solution-group-1 there and solution-group-2 in the text and so on. WP:LEADLENGTH is pretty clear on how much compression there should be from body text to lead summary. Churn and change (talk) 00:06, 19 October 2012 (UTC)
 * The lead was not extensively discussed in the RfC, nor was it really a part of the original proposal. But it was a part of at least some responses.  I'm not seeing much in the way of consensus about what to do with it precisely, but I don't have a strong opinion about WP:LEADLENGTH.  It is clear how much there ought to be given the article length, but it's also not an absolute rule.  Given the discussion, I would contend that either maintaining the current length or slightly lessening it would be appropriate.  An editor suggested removing mention of how either set of solutions works entirely, focusing on the problem itself and the response from the academic community.  I, Jethrobot  drop me a line (note: not a bot!) 05:53, 22 October 2012 (UTC)
 * I think if there is no particular consensus we should just refer to the appropriate policy/guidelines as per WP:POLICY. -- Eraserhead1 &lt;talk&gt; 19:31, 22 October 2012 (UTC)


 * Splitting the article. Two issues I see: per WP:SPLIT splits are mostly to handle size issues, and at times to separate disparate content. The article isn't that big right now. Also, the "mathematical" objections to solution-group-1 are published largely in journals related to math teaching; so doesn't look like it is cutting-edge research or notable enough for an article of its own. The math analyses of the problem itself are typically in textbooks. I think the importance of the stuff is exaggerated by the dispute. Churn and change (talk)
 * I agree that a split would not be appropriate at present, but I think our decision should state that there is no prejudice against future discussion of splitting the article pending additional significant coverage. Currently, I see these articles supporting such a split due to recognition of different problem parameters or different approaches: , , and some others (including one outside of the mathematics discipline).  I don't think these are necessarily "cutting edge," (some have been around for ~5 years) but for now, these discussions must stay in the current article.  I, Jethrobot  drop me a line (note: not a bot!) 05:53, 22 October 2012 (UTC)
 * Fine, it was only a thought. -- Eraserhead1 &lt;talk&gt; 19:29, 22 October 2012 (UTC)
 * Those articles are actually tutorial stuff. The journals are meant for undergrad students or for those teaching them. The sources are, by our definition, primary (original research) and secondary-source coverage is probably nonexistent. Quality is a concern, since the journals do not have impact factors and the authors aren't particularly notable. My main worry with these primary sources, more than policy issues, is that the editors there will almost certainly have disputes over interpretation, due weight and so on. I would be be fine including their explanations but not the criticism of vos Savant; that is from the point of view of a student-and-teacher-oriented article. Churn and change (talk) 06:09, 22 October 2012 (UTC)


 * An added suggestion from my side: one editor did point out a solution in a secondary source that doesn't use probability at all.
 * Just assume car is behind door 1.
 * Let us say subject picks door 1. Monty will open door 2 or door 3. In any case, switching means participant loses.
 * Let us say subject picks door 2. Monty will open door 3. Participant wins when switching.
 * Let us say subject picks door 3. Monty will open door 2. Participant wins when switching.
 * So, with switching, participant wins in 2 cases and loses in 1. Better than half-half.
 * That description is accurate for the specific problem, avoids probabilities altogether, and provides the right answer. With a figure, it can be put through even better (fig is there in the source). I think that should come first, before vos Savant's solution which does use probability, even though in a simple way. Not OR, since this is from one of the sources mentioned by somebody. Churn and change (talk)
 * It is good that there exists a description of the problem that avoids complex discussions of probability, but I cannot help but feel like a significant minority of editors (at least) will object to this on the basis of that it doesn't state problem parameters adequately enough or that it is grossly oversimplified. Basically, I think it will cause persistent content disputes despite it being reliably sourced.  That said, I still think both consensus and the policies we've cited above support such a description, but I am trying to be realistic and remind us of our goals with closing this RfC.  Also, can you point me to the source of this description?  I couldn't find it on the talk page.  I, Jethrobot  drop me a line (note: not a bot!) 05:53, 22 October 2012 (UTC)
 * It is Krauss&Wang (I have hosted a link to it above), page 5. Rick Block brought it up somewhere in those tangled threads, and, looking at the history here, will almost certainly bring it up again. Thought might as well support him on this one, since it looks fairly fine. My description is perhaps way too simple, but the figure and description in the original is complete enough for the exact problem presented (though, of course, this gets harder if we increase the number of doors and so on). Churn and change (talk) 06:02, 22 October 2012 (UTC)
 * OK, having taking a closer look at the original source, I think the problem is laid out pretty well. Many editors supported a simpler framing of the problem, and also emphasized the need to clarify the standard problem in the article, and so I think this could work to address those points in the RfC.  I, Jethrobot  drop me a line (note: not a bot!) 20:47, 22 October 2012 (UTC)


 * As it is written, Proposal 2 did not achieve consensus. I think it should also be noted that many editors did not agree to either proposal, though the reasons for those disagreements varied variously.  I think one of the strongest neither supporters stated that the problem was that too much weight was being given to the "simple" vs. "conditional" debate in either one, and that because the point of the RfC was to reduce content disputes, the proposals were self-defeating.  The RfC does not seem to be a no consensus ruling, but many editors felt the proposals were inadequate solutions to the stated problem.  I, Jethrobot  drop me a line (note: not a bot!) 05:53, 22 October 2012 (UTC)
 * Yes, I agree. Prop 2 is dead. I also agree the article has many other problems (dead refs, duplications, odd section ordering, and what not). We could probably add a passing reference to those, since reducing content dispute is seemingly also our charter. We probably should avoid the simple/complex judgmental formulation, instead using our own names for the various solutions. Churn and change (talk) 06:14, 22 October 2012 (UTC)
 * I'm not sure how much over-thinking and dispute resolving we want to do, I think a fairly straight close (but obviously not a vote close) would probably be best. I agree on proposition 2. -- Eraserhead1 &lt;talk&gt; 19:29, 22 October 2012 (UTC)
 * I think whatever we have agreement on with regards to the solutions and their presentation (and policies and guidelines backing us), we should probably present. For a basic close of the RFC, they wouldn't need three editors; the conclusion was pretty obvious. I think unless we clearly present our interpretation, editors there will have disputes over what the RFC and its closing summary meant. Churn and change (talk) 20:35, 22 October 2012 (UTC)
 * Fair enough. -- Eraserhead1 &lt;talk&gt; 06:36, 23 October 2012 (UTC)


 * Churn, you already brought this up, but I agree that a renaming of the solutions is also fitting. I think the term "solutions for the standard problem" or something else that describes what the solution is intending to solve rather than qualifying how the solution measures up to other solutions.  Hence, "simple solutions" will have to go.  Another editor also brought up that the word "approaches" for both the conditional and standard problem might be better here to avoid conflict, but I didn't get the sense that the word "approaches" was used often in the reliable sources.  I believe, as Eraserhead1 has said, I am overthinking this.  So, perhaps changing it would not be a big deal.  I, Jethrobot  drop me a line (note: not a bot!) 13:43, 23 October 2012 (UTC)
 * Sounds good. -- Eraserhead1 &lt;talk&gt; 20:27, 24 October 2012 (UTC)

I think I will plan to present a full closing rationale on Monday or Tuesday next week. -- Eraserhead1 &lt;talk&gt; 20:27, 24 October 2012 (UTC)
 * Would like one or both of us to look it over before it is finalized? (I completely understand if you'd rather not-- we've sort of discussed this one to death.)  I, Jethrobot  drop me a line (note: not a bot!) 06:17, 25 October 2012 (UTC)
 * I think I'd rather not do that, discussing it has been good, but at the end of the day I think we have to make individual decisions. -- Eraserhead1 &lt;talk&gt; 06:52, 25 October 2012 (UTC)