# Is there mathematical substance to the claim that diversity trumps ability? [closed]

In a 2004 article entitled Groups of diverse problem solvers can outperform groups of high-ability problem solvers, L. Hong and S. Page argued that "diversity trumps ability" and provided a mathematical theorem to support their conclusion. In his 2007 book, Page added that "$\ldots$ the veracity of the diversity trumps ability claim is not a matter of dispute. It's true, just as $1+1=2$ is true", apparently referring to the said theorem.

In a 2014 article Does diversity trump ability?, A. Thompson provided a counterexample to the theorem of Hong and Page. In a subsequent exchange of letters, Hong and Page pointed out that Thompson missed a hypothesis that bars Thompson's counterexample, and Thompson retorted that the hypothesis was not given in the 2004 article.

All this surely boosts readership but it still leaves the purely mathematical and therefore educational question unanswered: is there nontrivial mathematical content to the Hong-Page theorem (once all the hypotheses are in place, that is)?

• I think this question should be on math.stackexchange. The justification "mathematical and therefore educational" is not sufficient, or we would end up as a math.stackexchange clone. – Steven Gubkin Dec 25 '14 at 14:34
• @Steven, the issue of multiculturalism and diversity is the burning issue in american education today. Thompson challenged the research by Hong and Page essentially because, as she claims, her children were not learning anything in school, due to what she feels are misplaced priorities in education. The question is therefore appropriate for the education site. If you feel it should be improved please make appropriate suggestions. – Mikhail Katz Dec 25 '14 at 16:21
• Perhaps you could summarize the educational content of the two articles, and distill an education question out of this? Currently the question seems to be asking for an opinion about the worth and veracity of a theorem, which is not a question about education. – Steven Gubkin Dec 25 '14 at 17:30
• @StevenGubkin, I have insufficient expertise in statistics to evaluate this. Doing the kind of evaluation you are suggesting is precisely what I was hoping to see in an answer. – Mikhail Katz Dec 26 '14 at 8:06
• Until recently, a good question might have been: How does the Hong/Page article inform decisions in the world of (mathematics) education? But a good answer is provided by Thompson's very readable article: The Hong/Page piece is not sound in its methodology. At all. The mathematical content can all be found in the Thompson article, where it is written up clearly. Mathematically, the role of randomness in algorithms is of nontrivial interest. (But cf. @StevenGubkin comments above.) With respect to "diversity" as it is understood in the social sciences: Hong/Page's work is inconsequential. – Benjamin Dickman Dec 26 '14 at 8:38