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COMPARISON OF THE POLAR DECISION RULES FOR VARIOUS TYPES OF DISTRIBUTIONS

机译：各种分布的极地决定规则的比较

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摘要

We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilite des decisions rendues a la pluralite des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A decision rule is optimal if it maximizes the probability of the group to make a correct choice. In this paper we assume the correctness probabilities of the experts to be independent random variables, selected from some given distribution. Moreover, the ranking of the members in the team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns.
机译：我们关注的是二分法选择模型，该模型可以追溯到Condorcet（1785年；《对应用程序进行决策的可能性》，巴黎的复数形式）。要求一组专家从两种选择中选择一种，而其中一种被认为是正确的。替代方案可能与各种各样的领域有关。决策规则将成员的个人意见转化为集体决策。如果决策规则可以最大程度地提高小组做出正确选择的可能性，则它是最佳选择。在本文中，我们假设专家的正确性概率是从某些给定分布中选择的独立随机变量。此外，团队成员的排名是（至少部分）已知的。因此，可以遵循基于该排名的规则。极不同的规则是专家规则和多数规则。在一系列论文中比较了两个极规则最优的概率。本文的主要目的是概述结果，为这些概率提供精确的公式或估计。我们考虑了各种分布，并表明对于所有这些分布，两个极性规则的概率的渐近行为遵循相同的模式。

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