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Arrow's Theorem for One-Dimensional Single-Peaked Preferences

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Author Info
Ehlers, Lars
Storcken, Ton (METEOR)

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Abstract

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow''s requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter’s preference is strictly quasi-concave.

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 043.

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Date of creation: 2007
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Handle: RePEc:dgr:umamet:2007043

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Keywords: mathematical economics;

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  1. 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. [Downloadable!]
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  2. Lars Ehlers & John A. Weymark, 2003. "Candidate stability and nonbinary social choice," Economic Theory, Springer, vol. 22(2), pages 233-243, 09. [Downloadable!] (restricted)
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  3. Sethuraman, Jay & Teo, Chung-Piaw & Vohra, Rakesh V., 2006. "Anonymous monotonic social welfare functions," Journal of Economic Theory, Elsevier, vol. 128(1), pages 232-254, May. [Downloadable!] (restricted)
  4. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December. [Downloadable!] (restricted)
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  5. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-37, July.
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  6. Bossert, W. & Weymark, J.A., 1991. "Generalized Median Social Welfare Functions," UBC Departmental Archives 91-29, UBC Department of Economics.
  7. Kim, K.H. & Roush, F.W., 1984. "Nonmanipulability in two dimensions," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 29-43, August. [Downloadable!] (restricted)
  8. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125 Elsevier. [Downloadable!] (restricted)
  9. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June. [Downloadable!] (restricted)
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  10. EHLERS, Lars & STORCKEN, Ton, 2002. "Arrow's Theorem in Spatial Environments," Cahiers de recherche 2002-03, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  11. Ehlers, Lars, 2001. "Independence axioms for the provision of multiple public goods as options," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 239-250, March. [Downloadable!] (restricted)
  12. Le Breton, M. & Weymark, J.A., 1991. "An Introduction to Arrovian Social Welfare Functions on Economic and Political Domains," UBC Departmental Archives 91-28, UBC Department of Economics.
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