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Single-Peaked Choice

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  • BOSSERT, Walter
  • PETERS, Hans

Abstract

Single-peaked preferences have played an important role in the literature ever since they were used by Black (1948) to formulate a domain restriction that is sufficient for the exclusion of cycles according to the majority rule. In this paper, we approach single-peakedness from a choice-theoretic perspective. We show that the well-known axiom independence of irrelevant alternatives (a form of contraction consistency) and a weak continuity requirement characterize a class of single-peaked choice functions. Moreover, we examine the rationalizability and the rationalizability-representability of these choice functions.

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Bibliographic Info

Paper provided by Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 11-2006.

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Length: 21 pages
Date of creation: 2006
Date of revision:
Handle: RePEc:mtl:montec:11-2006

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Keywords: Single-peakedness; choice functions; rationalizability; representability;

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References

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  1. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
  2. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  3. Dutta, Bhaskar & Peters, Hans & Sen, Arunava, 2002. "Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 392-416, October.
  4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  5. Bossert, Walter, 1994. "Rational choice and two-person bargaining solutions," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 549-563, November.
  6. Le Breton, Michel & Weymark, John, 2002. "Arrovian Social Choice Theory on Economic Domains," IDEI Working Papers 143, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2003.
  7. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
  8. Salvador Barbera & Matthew Jackson, 1991. "A Characterization of Strategy-Proof Social Choice Functions for Economies with Pure Public Goods," Discussion Papers 964, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. EHLERS, Lars & STORCKEN, Ton, 2002. "Arrow's Theorem in Spatial Environments," Cahiers de recherche 2002-03, Universite de Montreal, Departement de sciences economiques.
  10. LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
  11. Peters Hans & Wakker Peter, 1994. "WARP Does Not Imply SARP for More Than Two Commodities," Journal of Economic Theory, Elsevier, vol. 62(1), pages 152-160, February.
  12. Miguel Angel Ballester & Guillaume Haeringer, 2006. "A Characterization of Single-Peaked Preferences," UFAE and IAE Working Papers 656.06, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  13. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  14. DEBREU, Gérard, . "Smooth preferences," CORE Discussion Papers RP -132, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
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Citations

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Cited by:
  1. Walter Bossert & Hans Peters, 2012. "Single-Plateaued Choice," Cahiers de recherche 05-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Walter Bossert & Hans Peters, 2013. "Single-Basined Choice," Cahiers de recherche 04-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer, vol. 36(2), pages 305-322, February.
  4. Özgür Kıbrıs, 2012. "A revealed preference analysis of solutions to simple allocation problems," Theory and Decision, Springer, vol. 72(4), pages 509-523, April.

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