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Majority judgment and strategy-proofness: a characterization

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  • Stefano Vannucci

    (University of Siena)

Abstract

Majority judgment as recently formulated and advocated by Balinski and Laraki in their influential monograph (Majority Judgment (2010)) is a method to aggregate profiles of judgments which are expressed in a common language consisting of a linearly ordered, and typically bounded, set of grades. It is shown that majority judgment thus defined is strategy-proof but not coalitionally strategy-proof on a very comprehensive class of rich single peaked preference domains. The proof relies on the key observation that a common bounded linear order of grades makes the set of gradings a product of bounded chains, which is a special instance of a bounded distributive lattice. Relying on the foregoing result, this paper also provides a simple characterization of majority judgment with an odd number of agents by anonymity, bi-idempotence and strategy-proofness on rich single peaked domains.

Suggested Citation

  • Stefano Vannucci, 2019. "Majority judgment and strategy-proofness: a characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 863-886, September.
    • Handle: RePEc:spr:jogath:v:48:y:2019:i:3:d:10.1007_s00182-019-00666-4
    DOI: 10.1007/s00182-019-00666-4
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    References listed on IDEAS

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    1. Janowitz, M. F., 1984. "On the semilattice of weak orders of a set," Mathematical Social Sciences, Elsevier, vol. 8(3), pages 229-239, December.
    2. Vannucci, Stefano, 2016. "Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 56-67.
    3. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
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    8. Michel Balinski & Rida Laraki, 2020. "Majority judgment vs. majority rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 429-461, March.
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    Cited by:

    1. Ernesto Savaglio & Stefano Vannucci, 2022. "Strategy-proof aggregation rules in median semilattices with applications to preference aggregation," Papers 2208.12732, arXiv.org.
    2. Stefano Vannucci, 2022. "Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem," Papers 2210.03200, arXiv.org.
    3. Ernesto Savaglio & Stefano Vannucci, 2021. "Strategy-Proof Aggregation Rules in Median Semilattices with Applications to Preference Aggregation," Department of Economics University of Siena 867, Department of Economics, University of Siena.

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    More about this item

    Keywords

    Strategy-proofness; Bounded distributive lattice; Single peakedness; Majority rule; Majority judgment;
    All these keywords.

    JEL classification:

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

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