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Single-peaked choice

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  • Walter Bossert

    ()

  • Hans Peters

    ()

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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File URL: http://hdl.handle.net/10.1007/s00199-008-0393-1
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 41 (2009)
Issue (Month): 2 (November)
Pages: 213-230

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Handle: RePEc:spr:joecth:v:41:y:2009:i:2:p:213-230

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Related research

Keywords: Single-peakedness; Choice functions; Rationalizability; Representability; D11; D71;

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References

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  1. LeBreton, M., 1994. "Arrovian Social Choice on Economic Domains," G.R.E.Q.A.M. 94a37, Universite Aix-Marseille III.
  2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  3. Miguel Ángel Ballester & Guillaume Haeringer, 2006. "A Characterization of Single-Peaked Preferences," Working Papers 273, Barcelona Graduate School of Economics.
  4. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-15, July.
  5. EHLERS, Lars & STORCKEN, Ton, 2002. "Arrow's Theorem in Spatial Environments," Cahiers de recherche 2002-03, Universite de Montreal, Departement de sciences economiques.
  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. 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.
  8. 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.
  9. 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.
  10. Bossert, Walter, 1994. "Rational choice and two-person bargaining solutions," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 549-563, November.
  11. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  12. Inada, Ken-Ichi, 1969. "The Simple Majority Decision Rule," Econometrica, Econometric Society, vol. 37(3), pages 490-506, July.
  13. Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
  14. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
  15. 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.
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Citations

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

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