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Top monotonicity: A common root for single peakedness, single crossing and the median voter result

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  • Barberà, Salvador
  • Moreno, Bernardo

Abstract

When members of a voting body exhibit single peaked preferences, pair-wise majority voting equilibria (Condorcet winners) always exist. Moreover, they coincide with the median(s) of the votersʼ most preferred alternatives. This important fact is known as the median voter result. Variants of it also apply when single-peakedness fails, but preferences verify other domain restrictions, such as single-crossing, intermediateness or order restriction. Austen-Smith and Banks (1999) also proved that the result holds under single-peakedness, for a wide class of voting rules that includes the majority rule as a special case, and conveniently redefined versions of a median. We extend and unify previous results. We propose a new domain condition, called top monotonicity, which encompasses all previous domains restrictions, allows for new ones and preserves a version of the median voter result for a large class of voting rules. We also show that top monotonicity arises in interesting economic environments.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:gamebe:v:73:y:2011:i:2:p:345-359
    DOI: 10.1016/j.geb.2011.02.004
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    References listed on IDEAS

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    Cited by:

    1. Daron Acemoglu & Georgy Egorov & Konstantin Sonin, 2012. "Dynamics and Stability of Constitutions, Coalitions, and Clubs," American Economic Review, American Economic Association, vol. 102(4), pages 1446-1476, June.
    2. Philippe De Donder & Francisco Martinez-Mora, 2015. "On the Political Economy of University Admission Standards," Discussion Papers in Economics 15/11, Department of Economics, University of Leicester.
    3. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 95-109, March.
    4. 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.
    5. repec:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0060-6 is not listed on IDEAS
    6. Fasil Alemante & Donald E. Campbell & Jerry S. Kelly, 2016. "Characterizing the resolute part of monotonic social choice correspondences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 765-783, October.
    7. 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.
    8. König, Tobias & Lausen, Tobias & Wagener, Andreas, 2016. "Image concerns and the political economy of publicly provided private goods," Discussion Papers, Research Unit: Market Behavior SP II 2016-214, Social Science Research Center Berlin (WZB).
    9. repec:spr:sochwe:v:50:y:2018:i:3:d:10.1007_s00355-017-1092-2 is not listed on IDEAS
    10. Gabrielle Demange, 2011. "Majority relation and median representative ordering," Working Papers halshs-00581310, HAL.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. repec:spr:sochwe:v:48:y:2017:i:4:d:10.1007_s00355-017-1033-0 is not listed on IDEAS

    More about this item

    Keywords

    Single peaked; Single crossing and intermediate preferences; Majority (Condorcet) winners;

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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