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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

Given a profile of preferences on a set of alternatives, a majority relation is a complete binary relation that agrees with the strict preference of a strict majority of these preferences whenever such strict strict majority is observed. We show that a majority binary 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 "the closest in the aggregate". This requires a definition of what it means for a pair of preferences to be closer to each other then another. We assume that this definition takes the form of a distance function defined over the set of all conceivable preferences. We identify a necessary and sufficient condition for such a distance to be minimized by the preference of the majority. This condition requires the distance to be additive with respect to a plausible notion of compromise between preferences. The well-known Kemeny distance between preference does satisfy this property. We also provide a characterization of the class of distances satisfying this property as numerical representations of a primitive qualitative proximity relation between preferences.

Suggested Citation

  • Mihir Bhattacharya & Nicolas Gravel, 2019. "Is the preference of the majority representative?," Working Papers hal-02281251, HAL.
    • Handle: RePEc:hal:wpaper:hal-02281251
    Note: View the original document on HAL open archive server: https://hal.science/hal-02281251
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    References listed on IDEAS

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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

    preferences; majority; dissimilarity; 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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