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Positively Responsive Collective Choice Rules And Majority Rule: A Generalization Of May'S Theorem To Many Alternatives

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  • Sean Horan
  • Martin J. Osborne
  • M. Remzi Sanver

Abstract

May's theorem shows that if the set of alternatives contains two members, an anonymous and neutral collective choice rule is positively responsive if and only if it is majority rule. We show that if the set of alternatives contains three or more alternatives only the rule that assigns to every problem its strict Condorcet winner satisfies the three conditions plus Nash's version of “independence of irrelevant alternatives” for the domain of problems that have strict Condorcet winners. We show also that no rule satisfies the four conditions for domains that are more than slightly larger.

Suggested Citation

  • Sean Horan & Martin J. Osborne & M. Remzi Sanver, 2019. "Positively Responsive Collective Choice Rules And Majority Rule: A Generalization Of May'S Theorem To Many Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(4), pages 1489-1504, November.
    • Handle: RePEc:wly:iecrev:v:60:y:2019:i:4:p:1489-1504
    DOI: 10.1111/iere.12394
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    Cited by:

    1. Bhattacharya, Mihir & Gravel, Nicolas, 2021. "Is the preference of the majority representative ?," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 87-94.
    2. Kirneva Margarita & N'u~nez Mat'ias, 2023. "Legitimacy of collective decisions: a mechanism design approach," Papers 2302.09548, arXiv.org, revised Oct 2023.
    3. Stergios Athanasoglou & Somouaoga Bonkoungou & Lars Ehlers, 2023. "Strategy-proof preference aggregation and the anonymity-neutrality tradeoff," Working Papers 519, University of Milano-Bicocca, Department of Economics.
    4. Mihir Bhattacharya & Nicolas Gravel, 2019. "Is the Preference of the Majority Representative?," Working Papers 1028, Ashoka University, Department of Economics.
    5. Josep Freixas & Montserrat Pons, 2021. "An extension and an alternative characterization of May’s theorem," Annals of Operations Research, Springer, vol. 302(1), pages 137-150, July.
    6. John Duggan, 2019. "Weak rationalizability and Arrovian impossibility theorems for responsive social choice," Public Choice, Springer, vol. 179(1), pages 7-40, April.
    7. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    8. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.

    More about this item

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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