pascaldeuxzero Next one's coming faster. | Merome a écrit :
[...] Ce qui fait la compétence d'une assemblée, c'est pas le QI cumulé de ses membres, c'est sa diversité ("la diversité cognitive d'un groupe est plus importante que la compétence individuelle de ses membres" : https://fr.wikipedia.org/wiki/Tirag [...] e_note-117 ) et le fait que ces membres confrontent leurs avis avec des gens qui ne pensent pas comme eux. [...]
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Je quote tout le paragraphe de la page wikipedia :
Citation :
D'autres travaux avancent que dans le contexte de la résolution d'un problème, la diversité cognitive d'un groupe est plus importante que la compétence individuelle de ses membres[117]. Ce résultat, appelé "le théorème de la prévalence de la diversité sur la compétence", énonce que, sous certaines conditions, une assemblée constituée des membres tirés au sort est plus performante pour résoudre un problème qu'une assemblée constituée des membres les plus compétents[118]. Ce résultat peut-être vu comme une extension des analyses de Nicolas de Condorcet sur les décisions prises par une assemblée par le vote majoritaire. La diversité cognitive désigne la diversité des façons de voir le monde, d'interpréter et de résoudre un problème ou de se représenter une situation. Cette diversité permet à un groupe de voir et d'attaquer un problème de plusieurs directions, alors qu'un groupe plus homogène aura tendance à explorer qu'un petit nombre de solutions possibles, et n'aura que peu de chances de trouver la meilleure solution. En principe, il n'est pas clair que les élections puissent garantir la diversité cognitive des représentants, puisque les candidats aux élections ont beaucoup de chances de partager certains traits de personnalité, ou d'autres caractéristiques, qui réduiront la diversité de l'assemblée[119]. En conséquence, même si la compétence individuelle des élus peut être élevée, la diversité de l'assemblée, et donc son efficacité ne serait pas optimale. À l'opposé dans une assemblée tirée au sort, la compétence des individus sera par définition moyenne, mais la diversité cognitive de l'assemblée est garantie. Donc, en plus des autres avantages potentiels du tirage au sort (égalité, protection contre la corruption, etc.), la sélection aléatoire des représentants présenterait également un avantage important pour la qualité de la délibération. D'autres chercheurs cependant questionnent la validité de ce résultat[120]. [...] [118]↑ Landemore, Hélène, "Deliberation, cognitive diversity, and democratic inclusiveness: an epistemic argument for the random selection of representatives.", Synthese 190.7 (2013): 1209-1231.
[118]↑ Lu Hong and Scott E. Page, "Groups of diverse problem solvers can outperform groups of high-ability problem solvers", PNAS (2004) 101 (46) 16385-16389; doi:10.1073/pnas.0403723101
[120]↑ Thompson, Abigail. "Does Diversity Trump Ability?." Notices of the AMS 61.9 (2014).
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J'ai cherché (un peu) mais je n'ai pas réussi à mettre la main sur la publication de Hong et Page. Par contre, j'ai trouvé l'article du Pr Abigail Thompson (une matheuse à UC Davis) dans lequel elle critique assez sévèrement le Hong-Page "theorem". Tout y passe : le modèle trop simpliste, les maths erronées, les fondements et la validité du "théorème" (indépendamment des maths), la non-transposabilité à des humains, au monde réel et donc la pertinence. Lien plus bas pour ceux qui veulent tout lire :
Citation :
Under careful scrutiny, however, the paper is seen to have essential and irreparable errors. The mathematical content of [1] is presented in two main sections. In the first of these, “A Computational Experiment,” the authors describe a computer simulation involving a collection of algorithms working together to solve a simple optimization problem. In this section the authors find that one collection of algorithms outperforms a second collection. They assign the label “diversity” to the first collection and the label “ability” to the second, and conclude that this is evidence that “diversity trumps ability.” In a subsequent section titled “A Mathematical Theorem,” the authors indicate that their analysis “ explores the logic behind the simulation results and provides conditions under which diversity trumps ability.” There are multiple problems in each of these sections. We can summarize the content of the theorem as follows: suppose that a group of people is set a task and the entire group’s performance is compared to that of just one member of the group working alone on the same task. Assume also that the conditions of the task are such that one person working alone can never complete the task, and that the whole group working together will always complete the task. It is neither surprising nor difficult to see that, in this situation, the group as a whole will outperform the individual. Yet this is the entire content of what Hong and Page call the “Mathematical Theorem,” Theorem 1 in [1]. We also point out several issues with the “Computational Experiment” section of [1]. Here the authors discuss computer simulations intended to illustrate and support the conclusions of Theorem 1. We demonstrate that Theorem 1 is unrelated to the computational experiment and that the experiment offers no support for the social applications proposed by the authors. [...] To summarize, the paper “Groups of diverse problem solvers can outperform groups of highability problem solvers” [1] contains a theorem that has neither mathematical content nor real-world applications, and a contrived computer simulation that illustrates the well-known fact that random algorithms are often effective. What the paper emphatically does not contain is information that can be applied to any real-world situation involving actual people.
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Source : Does Diversity Trump Ability? - An Example of the Misuse of Mathematics in the Social Sciences (Notices, October 2014)
Extraits d'une réaction :
Citation :
At issue is a claim by Lu Hong and Scott Page, including empirical evidence from computer simulation and even a mathematical “proof,” that “diversity trumps ability.” The idea is that when comparing performance of groups of agents working together to solve a problem, groups selected randomly from a “diverse” pool of agents of varying ability can perform better than groups comprised solely of the “best” individuals. “Diversity” is a fun word. It’s a magnet for controversy, particularly when, as in this case, it is conveniently poorly defined. But the notion that diversity might actually provably yield better results is certainly tantalizing, and is worth a close look. Unfortunately, upon such closer inspection, Abigail Thompson in the recent AMS Notices shows that not only is the mathematics in the paper incorrect, but even when reasonably corrected, the result is essentially just a tautology, with little if any actual “real world” interpretation or application. And the computer simulation, that ostensibly provides backing empirical evidence, ends up having no relevance to the accompanying mathematical theorem. The result is that Hong and Page’s central claim enjoys none of the rigorous mathematical justification that distinguished it from most of the literature on diversity research in the first place. And this is what annoys me: trying to make an overly simple-to-state claim– that is tenuous to begin with– about incredibly complex human behavior, and dressing it up with impressive-sounding mathematics. Which turns out to be wrong.
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Source : No, diversity does not generally trump ability, October 9, 2014
Une autre dans laquelle un autre mathématicien valide le travail de Thompson :
Citation :
It’s a model that has been used “to give a scientific veneer to the diversity field,” according to Professor Abigail Thompson, a mathematician at UC Davis. The problem is, she adds, the model is “an example of the misuse of mathematics in the social sciences.” Thompson makes that point in her peer-reviewed critique of the model published September by the American Mathematical Society. “The paper ‘Groups of diverse problem solvers can outperform groups of high ability problem solvers’ contains a theorem that has neither mathematical content nor real-world applications, and a contrived computer simulation that illustrates the well-known fact that random algorithms are often effective,” Thompson stated in her extensive rebuttal. “What the paper emphatically does not contain is information that can be applied to any real-world situation involving actual people.” Colgate University’s math department chair Professor Aaron Robertson, in an email to The College Fix, said that as a mathematician he corroborates Thompson’s work. Page and the co-author of his model, Loyola University Chicago economist Lu Hong, are two non-mathematicians who attempted to prove that diversity trumps ability “through a mathematical framework mired in unnecessary mathematical jargon,” Robertson said. “Hong and Page’s ‘study’ is routinely pointed to as scientific proof that diversity – in and of itself – is a sign of excellence. Because … science,” Robertson said. “We must make it known that Hong and Page’s ‘results’ are actually vacuous (or, at best, highly trivial) statements.”
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Un morceau de la réponse de Page :
Citation :
Within the Hong Page framework, a group’s collective potential to solve difficult problems depends on both ability (people with lots of tools) as well as diversity (people with distinct tools). Strong empirical evidence supports that hypothesis. Further, the Hong Page framework expands on the notion of ability as some sort of general capacity and in doing so provides a language with which intelligent, thoughtful people can discuss a variety of issues related to hiring, inclusivity, and opportunity. That, I believe, is worthy of Education News.
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Source : Mathematicians refute oft-cited ‘diversity trumps ability’ study, DECEMBER 5, 2014
Oui, ok. Si on prend des gens compétents, la diversité est un plus. Merci. 
Ultimes extraits pour la route (une réaction au papier de Thompson, la réponse de Page, la re-réponse de Thompson) :
Citation :
[...] Quote-checking during the review process could also have helped. This one from Page’s book [3] is displayed on the first page of the article and sets the stage for what is to follow: “…the veracity of the diversity trumps ability claim is not a matter of dispute. It’s true, just as 1+1=2 is true.” This appears to invite the reader to believe that Page claims to have in hand a mathematical result that can be fearlessly applied in social science settings to groups of people, and a remark in the same paragraph of the Notices article that the quote refers to work “ostensibly proving that a group picked on the basis of ‘diversity’ criteria outperforms one picked on the basis of ‘ability’” seems to confirm that interpretation. Had Page’s quote been checked for context, I am certain that there would have been insistence that the sentence following the excerpt also be included in the quote: “However, the claim applies to mathematical objects and not to people directly.” Page’s claims for the applicability of his “diversity trumps ability” assertion are actually highly qualified throughout his book. For example, right up front in his introduction (p. xxiii) Page states that, “My claims that diversity produces benefits rest on conditions. These conditions require, among other things, that diversity is relevant—we cannot expect that adding a poet to a medical research team would enable them to find a cure for the common cold.” This is far from the flat, unqualified endorsement of diversity over ability the reader might infer from the truncated quote. [...]
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Plus loin, par Page : Citation :
Second, and more troubling, the note accuses me of misusing mathematics, claiming that I imply that the mathematical results are somehow fact in the world of people. The accusation is baseless. In my book, I caution readers to apply mathematical models carefully, high-lighting the subtleties of moving from the starkness of mathematical logic to the richness of human interactions.
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Source : http://www.ams.org/notices/201501/rnoti-p9.pdf
Pour résumer :
- Les travaux de Hong et Page s'appuient sur une simulation, pas sur des individus. Les résultats mathématiques ne peuvent être considérés comme des faits dans le vrai monde.
- Le "théorème" Hong-Page est sujet à controverse, sa validité est discutée n'en est pas un.
- Dans tous les cas, les conclusions de Hong et Page reposent sur des conditions. La diversité joue un rôle mais n'est pas suffisante, elle ne peut être décorrelée des compétences.
Je trouve que ce "théorème" est présenté de façon bien superficielle sur wikipédia. Il ne s'agit que d'un modèle théorique dont la rigueur est discutable et la transposition des résultats dans la vraie vie est délicate. De plus, il s'appuie sur des conditions essentielles qui sont omises : diversité et compétences.
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