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A Characterization of Single-Peaked Preferences

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  • Miguel Ángel Ballester
  • Guillaume Haeringer

Abstract

We identify in this paper two conditions that characterize the domain of single-peaked preferences on the line in the following sense: a preference profile satisfies these two properties if and only if there exists a linear order L over the set of alternatives such that these preferences are single-peaked with respect L. The first property states that for any subset of alternatives the set of alternatives considered as the worst by all agents cannot contains more than 2 elements. The second property states that two agents cannot disagree on the relative ranking of two alternatives with respect to a third alternative but agree on the (relative) ranking of a fourth one.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 273.

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Date of creation: Jan 2006
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Handle: RePEc:bge:wpaper:273

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Keywords: Single-peaked preferences; lineal order;

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References

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  1. Salvador Barbera & Hugo Sonnenschein & Lin Zhou, 1990. "Voting by Committees," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 941, Cowles Foundation for Research in Economics, Yale University.
  2. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, Elsevier, vol. 3(4), pages 389-396, December.
  3. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, Springer, vol. 35(4), pages 437-455, January.
  4. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2489-2497, November.
  5. 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.
  6. Barbera, S. & Sonnenschein, H., 1988. "Voting By Quota And Committee," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 95-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  7. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
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Cited by:
  1. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer, Springer, vol. 41(2), pages 213-230, November.
  2. Vicki Knoblauch, 2008. "Recognizing One-Dimensional Euclidean Preference Profiles," Working papers, University of Connecticut, Department of Economics 2008-52, University of Connecticut, Department of Economics.
  3. Vicki Knoblauch, 2008. "Recognizing a Single-Issue Spatial Election," Working papers, University of Connecticut, Department of Economics 2008-26, University of Connecticut, Department of Economics.

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