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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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 73 (2011)
Issue (Month): 2 ()
Pages: 345-359

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Handle: RePEc:eee:gamebe:v:73:y:2011:i:2:p:345-359

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Web page: http://www.elsevier.com/locate/inca/622836

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

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References

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  1. 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.
  2. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  3. Miguel Ballester & Guillaume Haeringer, 2011. "A characterization of the single-peaked domain," Social Choice and Welfare, Springer, vol. 36(2), pages 305-322, February.
  4. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  5. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  6. 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.
  7. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  8. Gans, Joshua S. & Smart, Michael, 1996. "Majority voting with single-crossing preferences," Journal of Public Economics, Elsevier, vol. 59(2), pages 219-237, February.
  9. 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.
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Citations

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Cited by:
  1. Konstantin Sonin & Georgy Egorov & Daron Acemoglu, 2008. "Dynamics and Stability of Constitutions, Coalitions and Clubs," 2008 Meeting Papers 314, Society for Economic Dynamics.
  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. 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.
  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:hal:wpaper:halshs-00581310 is not listed on IDEAS
  6. Gabrielle Demange, 2011. "Majority relation and median representative ordering," PSE Working Papers halshs-00581310, HAL.

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