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Symmetric majority rules

Author

Listed:
  • Daniela Bubboloni

    (Dipartimento di Scienze per l'Economia e l'Impresa, Universita' degli Studi di Firenze)

  • Michele Gori

    (Dipartimento di Scienze per l'Economia e l'Impresa, Universita' degli Studi di Firenze)

Abstract

In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle. In particular, supposing that individuals and alternatives are exogenously partitioned into subcommittees and subclasses, we provide necessary and sufficient conditions for the existence of reversal symmetric majority rules that are anonymous and neutral with respect to the considered partitions. We also determine a general method for constructing and counting those rules and we explicitly apply it to some simple cases.

Suggested Citation

  • Daniela Bubboloni & Michele Gori, 2014. "Symmetric majority rules," Working Papers - Mathematical Economics 2014-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa, revised Mar 2015.
    • Handle: RePEc:flo:wpaper:2014-02
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    References listed on IDEAS

    as
    1. Michele Gori, 2014. "Selecting anonymous, neutral and reversal symmetric minimal majority rules," Working Papers - Mathematical Economics 2014-04, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    2. Daniela Bubboloni & Michele Gori, 2014. "Anonymous and neutral majority rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 377-401, August.
    3. Powers, R.C., 2010. "Maskin monotonic aggregation rules and partial anonymity," Economics Letters, Elsevier, vol. 106(1), pages 12-14, January.
    4. Campbell, Donald E. & Kelly, Jerry S., 2013. "Anonymity, monotonicity, and limited neutrality: Selecting a single alternative from a binary agenda," Economics Letters, Elsevier, vol. 118(1), pages 10-12.
    5. Campbell, Donald E. & Kelly, Jerry S., 2011. "Majority selection of one alternative from a binary agenda," Economics Letters, Elsevier, vol. 110(3), pages 272-273, March.
    6. Daniela Bubboloni & Michele Gori, 2013. "Anonymous, neutral and reversal symmetric majority rules," Working Papers - Mathematical Economics 2013-05, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    7. Antonio Quesada, 2013. "The majority rule with a chairman," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 679-691, March.
    8. Perry, Jonathan & Powers, Robert C., 2008. "Aggregation rules that satisfy anonymity and neutrality," Economics Letters, Elsevier, vol. 100(1), pages 108-110, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Bubboloni, Daniela & Gori, Michele, 2016. "On the reversal bias of the Minimax social choice correspondence," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 53-61.
    2. Bubboloni, Daniela & Gori, Michele, 2016. "Resolute refinements of social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 37-49.
    3. Alexander Karpov, 2017. "Preference Diversity Orderings," Group Decision and Negotiation, Springer, vol. 26(4), pages 753-774, July.
    4. Mostapha Diss & Michele Gori, 2022. "Majority properties of positional social preference correspondences," Theory and Decision, Springer, vol. 92(2), pages 319-347, March.
    5. Daniela Bubboloni & Michele Gori & Claudia Meo, 2024. "Symmetric mechanisms for two-sided matching problems," Papers 2404.01404, arXiv.org.
    6. Lirong Xia, 2022. "Most Equitable Voting Rules," Papers 2205.14838, arXiv.org, revised Jul 2023.
    7. Daniela Bubboloni & Michele Gori, 2018. "The flow network method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 621-656, December.
    8. Daniela Bubboloni & Michele Gori, 2021. "Breaking ties in collective decision-making," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 411-457, June.
    9. McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.
    10. Ali I. Ozkes & M. Remzi Sanver, 2021. "Anonymous, neutral, and resolute social choice revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 97-113, July.
    11. Lirong Xia, 2024. "Computing Most Equitable Voting Rules," Papers 2410.04179, arXiv.org.

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    More about this item

    Keywords

    social welfare function; anonymity; neutrality; reversal symmetry; majority; group theory.;
    All these keywords.

    JEL classification:

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

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