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.

中文翻译：

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公平投票规则

梅定理（1952）是社会选择的一个著名结果，它为多数人统治提供了基础。梅的对称性的关键假设（通常被认为是程序上的公平性要求）被授予选民相同角色的许多选择程序所违反。我们表明，梅的对称性假设的减弱使更丰富的规则集仍然可以平等地对待选民。我们证明了这样的规则可以使获胜的联盟所占的比例最小，该联盟包括人口的消失部分，但不少于人口规模的平方根。在方法论上，我们从群体理论中介绍了技术，并说明了它们在分析社会选择问题中的有用性。