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

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  • Salvador Barberà
  • Bernardo Moreno

Abstract

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 has been crucial in the development of public economics and political economy. However, it only provides a sufficient condition, and there are many examples in the literature of environments where voting equilibria exist even if single peakedness does not hold. Some of them correspond to instances where other relevant conditions, not necessarily connected with single

Suggested Citation

  • Salvador Barberà & Bernardo Moreno, 2010. "Top monotonicity: A common root for single peakedness, single crossing and the median voter result," Working Papers 297, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:297
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    References listed on IDEAS

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    2. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Michel Balinski & Rida Laraki, 2022. "Majority Judgment vs. Approval Voting," Operations Research, INFORMS, vol. 70(3), pages 1296-1316, May.
    4. 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.
    5. Dotti, Valerio, 2019. "Political Parties and Policy Outcomes. Do Parties Block Reforms?," MPRA Paper 100227, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. Michel Balinski & Rida Laraki, 2020. "Majority judgment vs. majority rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 429-461, March.
    9. 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.
    10. Riste Gjorgjiev & Dimitrios Xefteris, 2015. "Transitive supermajority rule relations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 299-312, October.
    11. Gabrielle Demange, 2017. "The stability of group formation," Revue d'économie politique, Dalloz, vol. 127(4), pages 495-516.
    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. Friedrichsen, Jana & König, Tobias & Lausen, Tobias, 2021. "Social Status Concerns and the Political Economy of Publicly Provided Private Goods," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 131(633), pages 220-246.
    14. 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.
    15. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    16. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    17. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    18. 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.
    19. Tanguiane, Andranick S., 2022. "Analysis of the 2021 Bundestag elections. 2/4. Political spectrum," Working Paper Series in Economics 152, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    20. 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.
    21. 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, WZB Berlin Social Science Center.
    22. Mor Nitzan & Shmuel Nitzan & Erel Segal-Halevi, 2018. "Flexible level-1 consensus ensuring stable social choice: analysis and algorithms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(3), pages 457-479, March.
    23. 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.
    24. Edith Elkind & Piotr Faliszewski & Piotr Skowron, 2020. "A characterization of the single-peaked single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 167-181, January.
    25. Valerio Dotti, 2021. "Reaching across the aisle to block reforms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 533-578, September.

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    More about this item

    Keywords

    Single peaked; single crossing and intermediate preferences; majority (Condorcet) winners;
    All these keywords.

    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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