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Majority relation and median representative ordering

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  • Gabrielle Demange

    (PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

Abstract

This paper presents results on the transitivity of the majority relation and the existence of a median representative ordering. Building on the notion of intermediate preferences indexed by a median graph, the analysis extends well-known results obtained when the underlying graph is a line. In contrast with other types of restrictions such as single-peakedness, intermediate preferences allow for a clear distinction between restrictions on the set of preferences characteristics and those on the set of alternatives.

Suggested Citation

  • Gabrielle Demange, 2011. "Majority relation and median representative ordering," PSE Working Papers halshs-00581310, HAL.
  • Handle: RePEc:hal:psewpa:halshs-00581310
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00581310
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    References listed on IDEAS

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    1. Hansen, Pierre & Thisse, Jacques-Francois, 1981. "Outcomes of voting and planning : Condorcet, Weber and Rawls locations," Journal of Public Economics, Elsevier, vol. 16(1), pages 1-15, August.
    2. Barberà, Salvador & Moreno, Bernardo, 2011. "Top monotonicity: A common root for single peakedness, single crossing and the median voter result," Games and Economic Behavior, Elsevier, vol. 73(2), pages 345-359.
    3. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    4. Bandelt, Hans-Jurgen, 1985. "Networks with condorcet solutions," European Journal of Operational Research, Elsevier, vol. 20(3), pages 314-326, June.
    5. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    6. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    7. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    8. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
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    Cited by:

    1. Berno Buechel, 2014. "Condorcet winners on median spaces," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 735-750, March.
    2. Puppe, Clemens, 2016. "The single-peaked domain revisited: A simple global characterization," Working Paper Series in Economics 97, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    3. Gabrielle Demange, 2017. "The stability of group formation," Revue d'économie politique, Dalloz, vol. 127(4), pages 495-516.

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    Keywords

    majority rule; median graph; tree; Condorcet winner; intermediate preferences;

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