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Majority relation and median representative ordering

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  • Gabrielle Demange

    (PSE - Paris-Jourdan Sciences Economiques - CNRS : UMR8545 - École des Hautes Études en Sciences Sociales (EHESS) - École des Ponts ParisTech (ENPC) - École normale supérieure [ENS] - Paris - Institut national de la recherche agronomique (INRA), EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

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.

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Bibliographic Info

Paper provided by HAL in its series PSE Working Papers with number halshs-00581310.

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Date of creation: Mar 2011
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Handle: RePEc:hal:psewpa:halshs-00581310

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

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  1. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
  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. Bandelt, Hans-Jurgen, 1985. "Networks with condorcet solutions," European Journal of Operational Research, Elsevier, vol. 20(3), pages 314-326, June.
  4. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  5. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  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. 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.
  8. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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Cited by:
  1. Berno Buechel, 2014. "Condorcet winners on median spaces," Social Choice and Welfare, Springer, vol. 42(3), pages 735-750, March.

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