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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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Paper provided by Universidad del CEMA in its series CEMA Working Papers: Serie Documentos de Trabajo. with number 237.

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Date of creation: Jul 2003
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Handle: RePEc:cem:doctra:237
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  1. Moulin,Hervi, 1989. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521360555, May.
  2. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  3. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy.
  4. Christian List, 2002. "A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions," Economics Series Working Papers 123, University of Oxford, Department of Economics.
  5. Persson, Torsten & Tabellini, Guido, 1997. "Political Economics and Macroeconomic Policy," CEPR Discussion Papers 1759, C.E.P.R. Discussion Papers.
  6. 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.
  7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  8. Donald E. Campbell & Jerry S. Kelly, 2003. "A strategy-proofness characterization of majority rule," Economic Theory, Springer, vol. 22(3), pages 557-568, October.
  9. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  10. Roger B. Myerson, 1996. "Fundamentals of Social Choice Theory," Discussion Papers 1162, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Barbera, S., 1995. "Notes on a Strategy-Proof Social Choice Functions," UFAE and IAE Working Papers 292.95, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  12. 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.
  13. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
  14. 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.
  15. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
  16. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, June.
  17. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
  18. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  19. Alejandro Neme & Jordi MassÔ & Salvador BarberÁ, 1999. "Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes," Social Choice and Welfare, Springer, vol. 16(2), pages 321-336.
  20. Salvador Barberà, 2001. "An introduction to strategy-proof social choice functions," Social Choice and Welfare, Springer, vol. 18(4), pages 619-653.
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