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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.

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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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  1. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
  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. 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.
  4. Roberts, Kevin W. S., 1977. "Voting over income tax schedules," Journal of Public Economics, Elsevier, vol. 8(3), pages 329-340, December.
  5. 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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