  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.

Theoretical Economics;Group Theory