User:Churn and change/Monty Hall problem

The rules

 * Policies: WP:V, WP:NPOV, WP:OR
 * Guidelines: WP:RS, WP:MOSINTRO, WP:LEAD, WP:UNDUE, WP:JARGON, WP:MTAA, WP:RFC
 * Essays: WP:BETTER, WP:AESA, WP:UPFRONT, WP:ASTONISH

Debate summary
The central question of the RFC was whether it was better to present what was termed the "simple solutions" to the Monty Hall problem, starting with the one from vos Savant, or whether it was better to present what was called the "more complete" solutions, which included the simple solutions and qualifications and elaborations on it, first. However the discussion went well beyond this issue, with many respondents commenting the dichotomy presented excluded better options. The simple-solution proponents stated these solutions were comprehensible to, and precise enough for, lay people. The complex-solution proponents stated the vos Savant solution, in particular, was riddled with imprecision in formulation and inaccuracies in the analysis.

Terminology concerns
Some objected to the terminology of simple and complex, and, agreeing to that, I will refer to the two sets of solutions as "first set" and "second set." Where needed, I will refer to each solution (vos Savant, Krauss & Wang one and so on) separately. The solutions in the first set, referred to here, are: Krauss & Wang, vos Savant, Carlton, Adams/Devlin and the multi-door point of view. The Krauss & Wang solution was referred to deep in a tangled thread by one of the editors; the others are already present in the article.

The Lead
The lead should reflect the body text and should not contain something not in it. Hence presenting the first set in the lead and second set in the body text is not allowed. WP:LEADLENGTH specifies length of lead, and how much the body text should be compressed to generate the lead. The RFC has produced no consensus on what should be in the lead; however, considering the body text is under dispute, that doesn't seem a concern.

Presentation order of solutions
The RFC veers around to the view the first set should be presented before the second. While some arguments from a one-off psychological study were presented to show people had trouble with the solutions, the general feel is we need to go with our understanding of what lay people think like. Adding to that, I see the best order as Krauss & Wang, vos Savant, Carlton, Adams/Devlin and the multi-door point of view, followed by the solutions of the second set. The Krauss & Wang solution, on page 5 of their paper, does not use probability, and is a simple enumeration of all possible scenarios of the problem and the results from switching and not switching. The figures in that paper compactly cover the solution space. One can argue technically probabilities are implied, but that is no objection; the solution needs no background in math.

The RFC discussed objections to Savant's solution, and seemed to settle more on accepting it as good enough for the lay person. I note in these footnotes of the closers' original discussion that the criticism is mostly in journals catering to undergraduates or math teachers, and are written with them in mind. These are not refutations of correctness, they are more objections from a math pedagogical point of view. Lack of math precision and lack of generalizability seem the main objections, and neither matter for the average Wikipedia reader. The solution is accurate for the problem posed, as mentioned in greater detail here. As such, criticism of Savant's solution does not meet our neutral-point-of-view policy, since the context of WP is different from that of a journal intended for math pedagogy.

General wording of the problem
The weight of arguments in the RFC indicates we should avoid words such as random, uniform, unbiased and so on in the lead and the initial sections. People do not talk of tossing an unbiased coin in a random or uniform way. They just refer to a "coin-toss result." Math teachers do use such words for precision, but WP is not a math encyclopedia. In sections farther down, where the article discusses solutions of the second set, the more precise terminology should be used. Adding to the arguments in the RFC, I will point out the extensions to the vos Savant formulation (Monty Fall and Monty Crawl of Rosenthal an example) should not be treated in great length because: 1. The sources are actually primary, containing new analysis, and 2. In many cases, the sources are in journals without even an impact factor, indicating they, in this case Math Horizons, are meant for a non-research readership, typically math undergrads and teachers (see footnotes from closers' original discussion). Editors should not provide too much weight to extensions used by teachers to help students learn concepts. WP is not a textbook.