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The Probability of Condorcet Cycles and Super-Majority Rules

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  • Yves Balasko

    (Department of Economics and Related Studies)

  • 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," Sciences Po publications info:hdl:2441/10273, Sciences Po.
  • Handle: RePEc:spo:wpmain:info:hdl:2441/10273
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    References listed on IDEAS

    as
    1. Kramer, Gerald H, 1973. "On a Class of Equilibrium Conditions for Majority Rule," Econometrica, Econometric Society, vol. 41(2), pages 285-297, March.
    2. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
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    4. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    5. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    6. DeMeyer, Frank & Plott, Charles R, 1970. "The Probability of a Cyclical Majority," Econometrica, Econometric Society, vol. 38(2), pages 345-354, March.
    7. Kenneth J. Arrow & Herve Raynaud, 1986. "Social Choice and Multicriterion Decision-Making," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262511754, December.
    8. 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.
    9. 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:

    1. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Consistent collective decisions under majorities based on difference of votes," Theory and Decision, Springer, vol. 80(3), pages 473-494, March.
    2. Estelle Cantillon & Antonio Rangel, 2002. "A graphical analysis of some basic results in social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 587-611.
    3. Mich Tvede & Hervé Crés, 2005. "Voting in assemblies of shareholders and incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 887-906, November.
    4. Eivind Stensholt, 2013. "What shall we do with the cyclic profile?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 229-262, January.
    5. Truchon, Michel, 1999. "La démocratie : oui, mais laquelle?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 75(1), pages 189-214, mars-juin.
    6. Roger Congleton, 2012. "The constitutional political economy of Gordon Tullock," Public Choice, Springer, vol. 152(1), pages 131-146, July.
    7. Hervé Crès & M. Utku Ünver, 2010. "Ideology and Existence of 50%-Majority Equilibria in Multidimensional Spatial Voting Models," Journal of Theoretical Politics, , vol. 22(4), pages 431-444, October.
    8. Roger D. Congleton, 2016. "Gordon Tullock’s implicit analytical history of government," Constitutional Political Economy, Springer, vol. 27(2), pages 179-193, June.
    9. Ngoie, Ruffin-Benoit M., 2012. "Choix social et partage équitable : Une analyse mathématique a posteriori des élections législatives et présidentielles de 2006 et 2011 en RDC [Social choice and fair sharing: An a posteriori mathe," MPRA Paper 64915, University Library of Munich, Germany.
    10. Vicki Knoblauch, 2015. "Two preference metrics provide settings for the study of properties of binary relations," Theory and Decision, Springer, vol. 79(4), pages 615-625, December.
    11. Mostapha Diss & Patrizia Pérez-Asurmendi, 2016. "Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support," Group Decision and Negotiation, Springer, vol. 25(5), pages 967-994, September.
    12. Tovey, Craig A., 1997. "Probabilities of Preferences and Cycles with Super Majority Rules," Journal of Economic Theory, Elsevier, vol. 75(2), pages 271-279, August.
    13. Vicki Knoblauch, 2014. "Preference, topology and measure," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 507-514, August.
    14. Mostapha Diss & Patrizia Pérez-Asurmendi, 2015. "Consistent collective decisions under majorities based on difference of votes," Working Papers halshs-01241996, HAL.
    15. 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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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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