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 modification of May's symmetry assumption allows for a far richer set of rules that still treat voters equally , but have minimal winning coalitions comprising a vanishing fraction of the population . We conclude that procedural fairness can coexist with the empowerment of a small minority of individuals . Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.
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.
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modification
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, but
. We show that such rules can
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. We conclude that procedural fairness can coexist with the empowerment of a small minority of individuals
, but not less than the square root of the population size