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Is the preference of the majority representative ?

Author

Listed:
  • Mihir Bhattacharya

    (Ashoka University)

  • Nicolas Gravel

    (CSH - Centre de sciences humaines de New Delhi - MEAE - Ministère de l'Europe et des Affaires étrangères - CNRS - Centre National de la Recherche Scientifique, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

We show that a majoritarian relation is, among all conceivable binary relations, the most representative of the profile of preferences from which it emanates. We define "the most representative" to mean that it minimizes the sum of distances between itself and the preferences in the profile for a given distance function. We identify a necessary and sufficient condition for such a distance to always be minimized by a majoritarian relation. This condition requires the distance to be additive with respect to a plausible notion of compromise between preferences. The well-known Kemeny distance does satisfy this property, along with many others. All distances that satisfy this property can be written as a sum of strictly positive weights assigned to the ordered pairs of alternatives by which any two preferences differ.

Suggested Citation

  • Mihir Bhattacharya & Nicolas Gravel, 2021. "Is the preference of the majority representative ?," Post-Print hal-03545861, HAL.
    • Handle: RePEc:hal:journl:hal-03545861
    DOI: 10.1016/j.mathsocsci.2021.04.001
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    References listed on IDEAS

    as
    1. 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.
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    Cited by:

    1. Hiroki Nishimura & Efe A. Ok, 2023. "Best Complete Approximations of Preference Relations," Papers 2311.06641, arXiv.org.

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    More about this item

    Keywords

    Binary relations; Majority; Distance; Aggregation;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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