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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, 2021. "Equitable Voting Rules," Econometrica, Econometric Society, vol. 89(2), pages 563-589, March.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:2:p:563-589
    DOI: 10.3982/ECTA17032
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    References listed on IDEAS

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    1. Robert E. Goodin & Christian List, 2006. "A Conditional Defense of Plurality Rule: Generalizing May's Theorem in a Restricted Informational Environment," American Journal of Political Science, John Wiley & Sons, vol. 50(4), pages 940-949, October.
    2. 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.
    3. Karol Życzkowski & Wojciech Słomczyński, 2014. "Square Root Voting System, Optimal Threshold and π," Studies in Choice and Welfare, in: Rudolf Fara & Dennis Leech & Maurice Salles (ed.), Voting Power and Procedures, edition 127, pages 127-146, Springer.
    4. Packel, Edward W., 1980. "Transitive permutation groups and equipotent voting rules," Mathematical Social Sciences, Elsevier, vol. 1(1), pages 93-100, September.
    5. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    6. 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.
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    Citations

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    Cited by:

    1. Bubboloni, Daniela & Gori, Michele & Meo, Claudia, 2025. "Resolute and symmetric mechanisms for two-sided matching problems," Journal of Mathematical Economics, Elsevier, vol. 118(C).
    2. Hans Gersbach, 2024. "Forms of new democracy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(4), pages 799-837, June.
    3. Stergios Athanasoglou & Somouaoga Bonkoungou, 2024. "Sequential unanimity voting rules for binary social choice," Papers 2402.13009, arXiv.org, revised Apr 2024.
    4. Manik Dhar & Kunal Mittal & Clayton Thomas, 2026. "Existence of Fair Resolute Voting Rules," Papers 2602.13894, arXiv.org.
    5. Kivinen, Steven, 2023. "On the manipulability of equitable voting rules," Games and Economic Behavior, Elsevier, vol. 141(C), pages 286-302.
    6. Steven Kivinen, 2024. "Weak Equity," Graz Economics Papers 2024-04, University of Graz, Department of Economics.
    7. Kivinen, Steven, 2024. "Equitable, neutral, and efficient voting rules," Journal of Mathematical Economics, Elsevier, vol. 115(C).
    8. Raschka, Robert, 2025. "A Single Relation Theory of Welfarist Social Evaluation," Journal of Mathematical Economics, Elsevier, vol. 121(C).
    9. Athanasoglou, Stergios & Bonkoungou, Somouaoga & Ehlers, Lars, 2025. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Games and Economic Behavior, Elsevier, vol. 152(C), pages 216-240.
    10. Hans Gersbach, 2022. "New Forms of Democracy," CESifo Working Paper Series 10134, CESifo.

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