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A Characterization of Single-Peaked Preferences

  • Miguel Ãngel Ballester
  • Guillaume Haeringer

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

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Date of creation: Sep 2015
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Handle: RePEc:bge:wpaper:273
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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. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
  3. 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.
  4. 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.
  5. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
  6. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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