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Equitable voting rules

Author

Listed:
  • Laurent Bartholdi
  • Wade Hann-Caruthers
  • Maya Josyula
  • Omer Tamuz
  • Leeat Yariv

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.

Suggested Citation

  • Laurent Bartholdi & Wade Hann-Caruthers & Maya Josyula & Omer Tamuz & Leeat Yariv, 2018. "Equitable voting rules," Papers 1811.01227, arXiv.org, revised Aug 2020.
  • Handle: RePEc:arx:papers:1811.01227
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    References listed on IDEAS

    as
    1. Estelle Cantillon & Antonio Rangel, 2002. "A graphical analysis of some basic results in social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 587-611.
    2. Mark Fey, 2004. "May’s Theorem with an infinite population," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 275-293, October.
    3. Packel, Edward W., 1980. "Transitive permutation groups and equipotent voting rules," Mathematical Social Sciences, Elsevier, vol. 1(1), pages 93-100, September.
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    More about this item

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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