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Condorcet Winners and the Paradox of Voting: Probability Calculations for Weak Preference Orders

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  • Jones, Bradford
  • Radcliff, Benjamin
  • Taber, Charles
  • Timpone, Richard

Abstract

That individual preferences may he aggregated into a meaningful collective decision using the Condorcet criterion of majority choice is one of the central tenets of democracy. But that individual preferences may not yield majority winners is one of the classic findings of the social choice literature. Given this problem, social choice theorists have attempted to estimate the probability of Condorcet winners, given certain empirical or theoretical conditions. We shall estimate the probabilities of Condorcet winners and intransitive aggregate orders for various numbers of individuals with strong or weak preference orders across various numbers of alternatives. We find, using computer simulation, a stark contrast between these estimates assuming strong individual preferences and the estimates allowing for individuals' indifference between pairs of alternatives. In contrast to earlier work, which depends on the strong-preference assumption, we suggest that the problem is most acute for small committee decision making and least acute for mass elections with few alternatives.

Suggested Citation

  • Jones, Bradford & Radcliff, Benjamin & Taber, Charles & Timpone, Richard, 1995. "Condorcet Winners and the Paradox of Voting: Probability Calculations for Weak Preference Orders," American Political Science Review, Cambridge University Press, vol. 89(1), pages 137-144, March.
    • Handle: RePEc:cup:apsrev:v:89:y:1995:i:01:p:137-144_09
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    Citations

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    Cited by:

    1. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    2. Kurrild-Klitgaard, Peter, 2001. "An Empirical Example of the Condorcet Paradox of Voting in a Large Electorate," Public Choice, Springer, vol. 107(1-2), pages 135-145, April.
    3. Kurrild-Klitgaard, Peter, 2018. "Trump, Condorcet and Borda: Voting paradoxes in the 2016 Republican presidential primaries," European Journal of Political Economy, Elsevier, vol. 55(C), pages 29-35.
    4. repec:spo:wpecon:info:hdl:2441/10286 is not listed on IDEAS
    5. Peter Kurrild-Klitgaard, 2014. "Empirical social choice: an introduction," Public Choice, Springer, vol. 158(3), pages 297-310, March.
    6. repec:hal:wpspec:info:hdl:2441/10286 is not listed on IDEAS
    7. repec:hal:spmain:info:hdl:2441/10286 is not listed on IDEAS
    8. Regenwetter, Michel & Marley, A. A. J. & Grofman, Bernard, 2002. "A general concept of majority rule," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 405-428, July.
    9. 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.
    10. Hervé Crès, 2001. "Aggregation of coarse preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 507-525.
    11. Hervé Crès, 2000. "Aggregation of Coarse Preferences," SciencePo Working papers Main hal-01064879, HAL.
    12. Hervé Crès, 2000. "Aggregation of Coarse Preferences," SciencePo Working papers hal-01064879, HAL.
    13. Kurrild-Klitgaard, Peter & Duminski, Emily & Horndrup, Søren Nikolai, 2023. "Demokratiets vilkårlighed: En analyse af forekomsten af valgparadokser ved tre folketingsvalg [The arbitrariness of democracy: An analysis of the occurrence of voting paradoxes in three Danish parl," MPRA Paper 118922, University Library of Munich, Germany.
    14. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
    15. Salvatore Barbaro, 2021. "A social-choice perspective on authoritarianism and political polarization," Working Papers 2108, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    16. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    17. Edith Elkind & Jérôme Lang & Abdallah Saffidine, 2015. "Condorcet winning sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 493-517, March.
    18. Johannes Pollak, 2004. "Democracy and the European Constitution: Majority Voting and Small Member States," The Constitutionalism Web-Papers p0019, University of Hamburg, Faculty for Economics and Social Sciences, Department of Social Sciences, Institute of Political Science.
    19. Richards, Diana, 1998. "Mutual knowledge structures and social coordination: a knowledge-induced equilibrium," Bulletins 7478, University of Minnesota, Economic Development Center.
    20. Mehdi Feizi & Rasoul Ramezanian & Saeed Malek Sadati, 2020. "Borda paradox in the 2017 Iranian presidential election: empirical evidence from opinion polls," Economics of Governance, Springer, vol. 21(2), pages 101-113, June.
    21. Franz Dietrich, 2004. "Terrorism Prevention: A General Model," Others 0404001, University Library of Munich, Germany.
    22. Meszerics, Tamás, 1997. "Stratégiai viselkedés és bizottsági döntés [Strategic behaviour and committee decison]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 687-697.
    23. Lepelley, Dominique & Martin, Mathieu, 2001. "Condorcet's paradox for weak preference orderings," European Journal of Political Economy, Elsevier, vol. 17(1), pages 163-177, March.
    24. 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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