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Single-Crossing, Strategic Voting and the Median Choice Rule

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  • Alejandro Saporiti

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  • 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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Suggested Citation

  • Alejandro Saporiti & Fernando Tohmé, 2006. "Single-Crossing, Strategic Voting and the Median Choice Rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 363-383, April.
  • Handle: RePEc:spr:sochwe:v:26:y:2006:i:2:p:363-383
    DOI: 10.1007/s00355-006-0098-y
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    References listed on IDEAS

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    2. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
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    Citations

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    Cited by:

    1. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    2. Maria Gallego & David Scoones, 2011. "Intergovernmental negotiation, willingness to compromise, and voter preference reversals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(3), pages 591-610, April.
    3. 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.
    4. Dietrich, Franz & List, Christian, 2010. "Majority voting on restricted domains," Journal of Economic Theory, Elsevier, vol. 145(2), pages 512-543, March.
    5. Robert Bredereck & Jiehua Chen & Gerhard Woeginger, 2013. "A characterization of the single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 989-998, October.
    6. Barberà, Salvador & Moreno, Bernardo, 2011. "Top monotonicity: A common root for single peakedness, single crossing and the median voter result," Games and Economic Behavior, Elsevier, vol. 73(2), pages 345-359.
    7. Alejandro Saporiti, 2005. "On the existence of Nash equilibrium in electoral competition," Game Theory and Information 0504005, EconWPA.
    8. Mridu Goswami, 2015. "Non fixed-price trading rules in single-crossing classical exchange economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 389-422, February.
    9. Cressman, Ross & Gallego, Maria, 2009. "On the ranking of bilateral bargaining opponents," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 64-83, July.
    10. Martínez-Mora Francisco & Puy M. Socorro, 2012. "Asymmetric Single-peaked Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-26, December.
    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.
    12. Fan-Chin Kung, 2015. "Sorting out single-crossing preferences on networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 663-672, March.
    13. 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).
    14. Morales, Dolores Romero & Vermeulen, Dries, 2009. "Existence of equilibria in a decentralized two-level supply chain," European Journal of Operational Research, Elsevier, vol. 197(2), pages 642-658, September.
    15. Doghmi Ahmed, 2014. "Nash Implementation in Rationing Problems with Single-Crossing Preferences," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 1-6, July.
    16. Alejandro Saporiti, 2006. "Strategic voting on single-crossing domains," The School of Economics Discussion Paper Series 0617, Economics, The University of Manchester.
    17. 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.

    More about this item

    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 Formulation and Implementation

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