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Single-Crossing, Strategic Voting and the Median Choice Rule

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Author Info
Alejandro Saporiti
Fernando Tohmé

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Abstract

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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Related research
Keywords: Single-crossing; order-restriction; median voter; strategyproofness.;

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Find related papers by JEL classification:
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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).
  2. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March. [Downloadable!] (restricted)
  3. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
  4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401.
    Other versions:
  5. 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. [Downloadable!]
  6. Persson, Torsten & Tabellini, Guido, 1997. "Political Economics and Macroeconomic Policy," CEPR Discussion Papers 1759, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  7. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December. [Downloadable!] (restricted)
  8. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  9. Christian List, 2002. "A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions," Economics Series Working Papers 123, University of Oxford, Department of Economics. [Downloadable!]
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  10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Bossert, W. & Weymark, J.A., 1991. "Generalized Median Social Welfare Functions," UBC Departmental Archives 91-29, UBC Department of Economics.
  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. [Downloadable!] (restricted)
  14. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October. [Downloadable!] (restricted)
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  15. Roger B. Myerson, 1996. "Fundamentals of Social Choice Theory," Discussion Papers 1162, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  16. Salvador Barberà, 2001. "An introduction to strategy-proof social choice functions," Social Choice and Welfare, Springer, vol. 18(4), pages 619-653. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. Donald E. Campbell & Jerry S. Kelly, 2003. "A strategy-proofness characterization of majority rule," Economic Theory, Springer, vol. 22(3), pages 557-568, October. [Downloadable!] (restricted)
  19. Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
    Other versions:
  20. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alejandro Saporiti, 2007. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP48, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
  2. Romero Morales,Dolores & Vermeulen,Dries, 2005. "Equilibrium plans in constrained environments," Research Memoranda 001, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  3. Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy. [Downloadable!]
    Other versions:
  4. Alejandro Saporiti, 2005. "On the existence of Nash equilibrium in electoral competition," Game Theory and Information 0504005, EconWPA. [Downloadable!]
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