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Positively Responsive Collective Choice Rules and Majority Rule : A Generalization of May’s Theorem to Many Alternatives

Author

Listed:
  • Sean HORAN
  • Martin J. OSBORNE
  • M. Remzi SANVER

Abstract

A collective choice rule selects a set of alternatives for each collective choice problem. Suppose that the alternative x is in the set selected by a collective choice rule for some collective choice problem. Now suppose that x rises above another selected alternative y in some individual’s preferences. If the collective choice rule is “positively responsive”, x remains selected but y is no longer selected. 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 (May 1952). If the set of alternatives contains three or more members, a large set of collective choice rules satisfy these three conditions. We show, however, that in this case 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. Further, no rule satisfies the four conditions for the domain of all preference relations.

Suggested Citation

  • Sean HORAN & Martin J. OSBORNE & M. Remzi SANVER, 2018. "Positively Responsive Collective Choice Rules and Majority Rule : A Generalization of May’s Theorem to Many Alternatives," Cahiers de recherche 03-2018, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:03-2018
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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. Salvatore Barbaro, 2024. "Electoral Methods and Political Polarization," Working Papers 2411, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    8. 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.
    9. 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

    Keywords

    Majority rule; Condorcet winner; May's theorem; positive responsiveness; Nash independence;
    All these keywords.

    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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