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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

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

  • Bernardo Moreno

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

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 (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.

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File URL: http://webdeptos.uma.es/THEconomica/malagawpseries/Papers/METCwp2008-9.pdf
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Bibliographic Info

Paper provided by Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center in its series Working Papers with number 2008-9.

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Length: 23 pages
Date of creation: May 2008
Date of revision:
Handle: RePEc:mal:wpaper:2008-9

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Keywords: Single peaked; single crossing and intermediate preferences; majority (Condorcet) winners;

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  1. Epple, Dennis & Romano, Richard E., 1996. "Ends against the middle: Determining public service provision when there are private alternatives," Journal of Public Economics, Elsevier, vol. 62(3), pages 297-325, November.
  2. David Cantala, 2004. "Choosing the level of a public good when agents have an outside option," Social Choice and Welfare, Springer, vol. 22(3), pages 491-514, 06.
  3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  4. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  5. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer, vol. 36(2), pages 305-322, February.
  6. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
  8. Stiglitz, J. E., 1974. "The demand for education in public and private school systems," Journal of Public Economics, Elsevier, vol. 3(4), pages 349-385, November.
  9. 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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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 1446-76, June.
  2. 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.
  3. repec:hal:wpaper:halshs-00581310 is not listed on IDEAS
  4. Gabrielle Demange, 2012. "Majority relation and median representative ordering," SERIEs, Spanish Economic Association, vol. 3(1), pages 95-109, March.
  5. 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.
  6. 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.

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