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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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    References listed on IDEAS

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    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.
    2. Walter Bossert & Burak Can & Conchita D’Ambrosio, 2016. "Measuring rank mobility with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 917-931, April.
    3. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 95-109, March.
    4. Benjamin Hadjibeyli & Mark C. Wilson, 2019. "Distance rationalization of anonymous and homogeneous voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 559-583, March.
    5. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    6. Lerer, Ehud & Nitzan, Shmuel, 1985. "Some general results on the metric rationalization for social decision rules," Journal of Economic Theory, Elsevier, vol. 37(1), pages 191-201, October.
    7. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    8. repec:hal:pseose:halshs-00670854 is not listed on IDEAS
    9. Farkas, Daniel & Nitzan, Shmuel, 1979. "The Borda Rule and Pareto Stability: A Comment," Econometrica, Econometric Society, vol. 47(5), pages 1305-1306, September.
    10. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2012. "Rationalizations of Condorcet-consistent rules via distances of hamming type," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 891-905, October.
    11. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    12. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    13. Suzumura, Kotaro, 2001. "Pareto principles from Inch to Ell," Economics Letters, Elsevier, vol. 70(1), pages 95-98, January.
    14. Can, B. & Storcken, A.J.A., 2015. "Comparing orders, rankings, queues, tournaments and lists," Research Memorandum 020, Maastricht University, Graduate School of Business and Economics (GSBE).
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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

    Majority; Distance; Binary Relation; 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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