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The Probability of Condorcet Cycles and Super-Majority Rules

Author

Listed:
  • Yves Balasko

    (Department of Economics and Related Studies - University of York [York, UK])

  • Hervé Crès

Abstract

Majority voting aggregates individual preference profiles into a binary relation on the set of alternatives. Condorcet cycles are cycles of the aggregated binary relation. We show that the relative volume of the subset of the (n!−1)-simplex that represents profile distributions such that the aggregated preferences display Condorcet cycles is a decreasing function of the super majority levelτbounded by the expressionThis expression shows that Condorcet cycles become rare events for super majority rules larger than 53%.

Suggested Citation

  • Yves Balasko & Hervé Crès, 1997. "The Probability of Condorcet Cycles and Super-Majority Rules," Post-Print hal-03458336, HAL.
    • Handle: RePEc:hal:journl:hal-03458336
    DOI: 10.1006/jeth.1996.2233
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03458336
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    References listed on IDEAS

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    1. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    2. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    3. DeMeyer, Frank & Plott, Charles R, 1970. "The Probability of a Cyclical Majority," Econometrica, Econometric Society, vol. 38(2), pages 345-354, March.
    4. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, April.
    5. Kelly, Jerry S, 1974. "Voting Anomalies, the Number of Voters, and the Number of Alternatives," Econometrica, Econometric Society, vol. 42(2), pages 239-251, March.
    6. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
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    Cited by:

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    3. Truchon, Michel, 1999. "La démocratie : oui, mais laquelle?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 75(1), pages 189-214, mars-juin.
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    6. Michel Regenwetter & James Adams & Bernard Grofman, 2002. "On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity," Theory and Decision, Springer, vol. 53(2), pages 153-186, September.

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