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Is the preference of the majority representative ?
[La préférence de la majorité est-elle représentative ?]

Author

Listed:
  • Mihir Bhattacharya

    (Ashoka University)

  • Nicolas Gravel

    (AMU - Aix Marseille Université, 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 ? [La préférence de la majorité est-elle représentative ?]," Post-Print hal-05074827, HAL.
    • Handle: RePEc:hal:journl:hal-05074827
    Note: View the original document on HAL open archive server: https://hal.science/hal-05074827v1
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