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Single-Crossing, Strategic Voting and the Median Choice Rule

  • Alejandro Saporiti

    ()

  • Fernando Tohmé

    ()

This paper studies the strategic foundations of the Representative Voter Theorem (Rothstein, 1991), also called the "second version" of the Median Voter Theorem. As a by-product, it also considers the existence of non-trivial strategy-proof social choice functions over the domain of single-crossing preference profiles. The main result presented here is that single-crossing preferences constitute a domain restriction on the real line that allows not only majority voting equilibria, but also non-manipulable choice rules. In particular, this is true for the median choice rule, which is found to be strategy-proof and group-strategic-proof not only over the full set of alternatives, but also over every possible policy agenda. The paper also shows the close relation between single-crossing and order-restriction. And it uses this relation together with the strategy-proofness of the median choice rule to prove that the collective outcome predicted by the Representative Voter Theorem can be implemented in dominant strategies through a simple mechanism in which, first, individuals select a representative among themselves, and then the representative voter chooses a policy to be implemented by the planner.

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File URL: http://hdl.handle.net/10.1007/s00355-006-0098-y
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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 26 (2006)
Issue (Month): 2 (April)
Pages: 363-383

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Handle: RePEc:spr:sochwe:v:26:y:2006:i:2:p:363-383
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  1. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  2. Torsten Persson & Guido Tabellini, . "Political Economics and Macroeconomic Policy," Working Papers 121, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  3. Ching, Stephen & Serizawa, Shigehiro, 1998. "A Maximal Domain for the Existence of Strategy-Proof Rules," Journal of Economic Theory, Elsevier, vol. 78(1), pages 157-166, January.
  4. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy.
  5. Alejandro Neme & Jordi MassÔ & Salvador BarberÁ, 1999. "Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 321-336.
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  11. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
  12. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  13. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  14. Roger B. Myerson, 1996. "Fundamentals of Social Choice Theory," Discussion Papers 1162, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
  16. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  17. Donald E. Campbell & Jerry S. Kelly, 2003. "A strategy-proofness characterization of majority rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(3), pages 557-568, October.
  18. 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.
  19. Barbera, S. & Masso, J. & Neme, A., 1992. "Voting Under Constraints," UFAE and IAE Working Papers 200.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
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