Econometrica · 2021 · Laurent Bartholdi、Wade Hann-Caruthers、Maya Josyula、Omer Tamuz、Leeat Yariv
中文摘要
梅氏定理 (May's theorem, 1952) 是社会选择理论中的一项著名结果, 它为多数规则奠定了基础。梅氏定理关键的对称性假设——常被视为一种程序公平要求——会被许多赋予投票者相同角色的选择程序所违背。我们证明, 对梅氏对称性假设加以弱化, 便可得到远为丰富的规则集合, 而这些规则仍然平等地对待投票者。我们证明, 这类规则的最小获胜联盟占人口的比例可以趋于零, 但其规模不得小于人口规模的平方根。在方法论上, 我们引入了群论中的技术, 并说明这些技术对于分析社会选择问题的有用性。
Abstract
May's theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.