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Top Monotonicity: A Common Root for Single Peakedness, Single Crossing and the Median Voter Result


  • Salvador Barberà

    () (Departament d'Economia i d'Historia Economica and CODE, Universitat Autonoma de Barcelona)

  • Bernardo Moreno

    () (Department of Economic Theory, Universidad de Málaga)


When the members of a voting body exhibit single peaked preferences, majority winners exist. Moreover, the median(s) of the preferred alternatives of voters is (are) indeed the majority (Condorcet) winner(s). This important result of Duncan Black (1958) has been crucial in the development of public economics and political economy, even if it only provides a sufficient condition. Yet, there are many examples in the literature of environments where voting equilibria exist and alternative versions of the median voter results are satisfied while single peakedness does not hold. Some of them correspond to instances where other relevant conditions, apparently not connected with single eakedness, are satisfied. For example preferences may satisfy the single-crossing property (Mirrlees, 1971, Gans and Smart, 1996, and Milgrom and Shannon, 1994), intermediateness (Grandmont, 1978) or order restriction (Rothstein, 1990). Still other interesting cases of existence of voting equilibria do not fall in any of these categories. We present a new and weak domain restriction which encompasses all the above mentioned ones, llows for new cases, still guarantees the existence of Condorcet winners and preserves a version of the median voter result. We illustrate how this new condition, that we call top monotonicity, arises naturally in different economic contexts.

Suggested Citation

  • Salvador Barberà & Bernardo Moreno, 2008. "Top Monotonicity: A Common Root for Single Peakedness, Single Crossing and the Median Voter Result," Working Papers 2008-9, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
  • Handle: RePEc:mal:wpaper:2008-9

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    References listed on IDEAS

    1. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    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.
    3. 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.
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    8. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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    13. David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 491-514, June.
    14. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 305-322, February.
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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. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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


    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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