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Single-Crossing, Strategic Voting and the Median Choice Rule

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  • Alejandro Saporiti
  • Fernando Tohmé

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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Bibliographic Info

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

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References

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  9. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
  10. 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).
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  14. Christian List, 2002. "A Possibility Theorem on Aggregation Over Multiple Interconnected Propositions," Economics Series Working Papers 123, University of Oxford, Department of Economics.
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  20. 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.
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Citations

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Cited by:
  1. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
  2. Robert Bredereck & Jiehua Chen & Gerhard Woeginger, 2013. "A characterization of the single-crossing domain," Social Choice and Welfare, Springer, vol. 41(4), pages 989-998, October.
  3. Romero Morales,Dolores & Vermeulen,Dries, 2005. "Equilibrium plans in constrained environments," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Islam, Jamal & Mohajan, Haradhan & Moolio, Pahlaj, 2010. "Methods of voting system and manipulation of voting," MPRA Paper 50854, University Library of Munich, Germany, revised 06 May 2010.
  5. Maria Gallego & David Scoones, 2011. "Intergovernmental negotiation, willingness to compromise, and voter preference reversals," Social Choice and Welfare, Springer, vol. 36(3), pages 591-610, April.
  6. Alejandro Saporiti, 2008. "Strategy-Proofness and Single-Crossing," Wallis Working Papers WP55, University of Rochester - Wallis Institute of Political Economy.
  7. Islam, Jamal & Mohajan, Haradhan & Moolio, Pahlaj, 2010. "Median voter model cannot solve all the problems of voting system," MPRA Paper 50696, University Library of Munich, Germany, revised 22 Feb 2011.
  8. Ross Cressman, Maria Gallego, 2005. "On the Ranking of Bilateral Bargaining Opponents," Working Papers eg0043, Wilfrid Laurier University, Department of Economics, revised 2005.
  9. Alejandro Saporiti, 2005. "On the existence of Nash equilibrium in electoral competition," Game Theory and Information 0504005, EconWPA.
  10. Franz Dietrich & Christian List, 2010. "Majority voting on restricted domains," LSE Research Online Documents on Economics 27902, London School of Economics and Political Science, LSE Library.
  11. Mridu Prabal Goswami, 2013. "Non Fixed-Price Trading Rules In Single-Crossing Classical Exchange Economies," Working Papers 1311, Ben-Gurion University of the Negev, Department of Economics.

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