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摘要翻译：
阿罗定理暗示一个满足传递性、帕累托原则（一致）和无关选择独立(IIA)的社会选择函数一定是独裁的。当非严格偏好被允许时，独裁社会选择函数被定义为存在一个严格偏好被遵循的单一选民的函数。这个定义允许许多不同的独裁功能。特别地，我们构造了不满足传递性和IIA的独裁函数的例子。因此，在非严格偏好的情况下，阿罗定理并没有提供满足传递性、帕累托原理和IIA的所有社会选择函数的完整表征。本文的主要结果为Arrow定理以及Wilson的后续结果提供了这样的刻画。特别地，我们通过给出一个函数满足传递性和IIA（以及Pareto原理）的精确当且仅当条件来加强Arrow和Wilson的结果。此外，我们还导出了满足这些条件的函数个数的公式。
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英文标题：
《Complete Characterization of Functions Satisfying the Conditions of
Arrow's Theorem》
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作者：
Elchanan Mossel and Omer Tamuz
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最新提交年份：
2011
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分类信息：
一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Economics 经济学
二级分类：Theoretical Economics 理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
Arrow's theorem implies that a social choice function satisfying Transitivity, the Pareto Principle (Unanimity) and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are allowed, a dictatorial social choice function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow's theorem, in the case of non-strict preferences, does not provide a complete characterization of all social choice functions satisfying Transitivity, the Pareto Principle, and IIA. The main results of this article provide such a characterization for Arrow's theorem, as well as for follow up results by Wilson. In particular, we strengthen Arrow's and Wilson's result by giving an exact if and only if condition for a function to satisfy Transitivity and IIA (and the Pareto Principle). Additionally, we derive formulas for the number of functions satisfying these conditions.
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PDF链接：
https://arxiv.org/pdf/0910.2465
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