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An Empirical Example of the Condorcet Paradox of Voting in a Large Electorate


  • Kurrild-Klitgaard, Peter


Social choice theory suggests that the occurrence of cyclical collective preferences should be a widespread phenomenon, especially in large groups of decision-makers. However, empirical research has so far failed to produce evidence of the existence of many real-world examples of such, and none in large electorates. This paper demonstrates the existence of a real cyclical majority in a poll of Danish voters' preferred prime minister, using pair-wise comparisons. This result is compared with those of a similar poll, but by using different voting methods, each resulting in different choices. The example demonstrates the empirical reality of cyclical collective preferences and the importance of the choice of institutions. Copyright 2001 by Kluwer Academic Publishers

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  • 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.
  • Handle: RePEc:kap:pubcho:v:107:y:2001:i:1-2:p:135-45

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    References listed on IDEAS

    1. van Deemen, Adrian M A & Vergunst, Noel P, 1998. "Empirical Evidence of Paradoxes of Voting in Dutch Elections," Public Choice, Springer, vol. 97(3), pages 475-490, December.
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    3. Plott, Charles R., "undated". "Axiomatic Social Choice Theory: An Overview and Interpretation," Working Papers 116, California Institute of Technology, Division of the Humanities and Social Sciences.
    4. Riker, William H., 1958. "The Paradox of Voting and Congressional Rules for Voting on Amendments," American Political Science Review, Cambridge University Press, vol. 52(2), pages 349-366, June.
    5. Klahr, David, 1966. "A Computer Simulation of the Paradox of Voting," American Political Science Review, Cambridge University Press, vol. 60(2), pages 384-390, June.
    6. John Dobra, 1983. "An approach to empirical studies of voting paradoxes: An update and extension," Public Choice, Springer, vol. 41(2), pages 241-250, January.
    7. DeMeyer, Frank & Plott, Charles R, 1970. "The Probability of a Cyclical Majority," Econometrica, Econometric Society, vol. 38(2), pages 345-354, March.
    8. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    9. 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.
    10. Gordon Tullock, 1981. "Why so much stability," Public Choice, Springer, vol. 37(2), pages 189-204, January.
    11. 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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    Blog mentions

    As found by, the blog aggregator for Economics research:
    1. Empirical social choice - special issue of "Public Choice"
      by Peter Kurrild-Klitgaard in Peter Kurrild-Klitgaard on 2014-02-17 15:15:00


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    Cited by:

    1. William Gehrlein, 2002. "Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences ," Theory and Decision, Springer, vol. 52(2), pages 171-199, March.
    2. repec:dau:papers:123456789/15122 is not listed on IDEAS
    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. Peter Kurrild-Klitgaard, 2012. "Modeling constitutional choice: reflections on The Calculus of Consent 50 years on," Public Choice, Springer, vol. 152(3), pages 407-413, September.
    5. Peter Kurrild-Klitgaard, 2015. "Classical Liberalism and Modern Political Economy in Denmark," Econ Journal Watch, Econ Journal Watch, vol. 12(3), pages 400–431-4, September.
    6. Matthew Harrison-Trainor, 2020. "An Analysis of Random Elections with Large Numbers of Voters," Papers 2009.02979,
    7. Mohajan, Haradhan, 2011. "Majority judgment in an election with Borda majority count," MPRA Paper 50846, University Library of Munich, Germany, revised 15 Sep 2011.
    8. Michel Balinski & Rida Laraki, 2015. "Majority Measures," Working Papers hal-01137173, HAL.
    9. Mostapha Diss & Eric Kamwa, 2019. "Simulations in Models of Preference Aggregation," Working Papers hal-02424936, HAL.
    10. Peter Kurrild-Klitgaard, 2014. "Picking a loser? A social choice perspective on the Danish government formation of 1975," Public Choice, Springer, vol. 158(3), pages 483-497, March.
    11. Richard Potthoff, 2013. "Simple manipulation-resistant voting systems designed to elect Condorcet candidates and suitable for large-scale public elections," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 101-122, January.
    12. Luigi Mittone, 2003. "The Condorcet paradox: an experimental approach to a voting process," CEEL Working Papers 0306, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
    13. Malthe Munkøe, 2014. "Cycles and instability in politics. Evidence from the 2009 Danish municipal elections," Public Choice, Springer, vol. 158(3), pages 383-397, March.
    14. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    15. Farzane Karami & Alireza B. Dariane, 2018. "Many-Objective Multi-Scenario Algorithm for Optimal Reservoir Operation Under Future Uncertainties," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(12), pages 3887-3902, September.
    16. Daniel Bochsler, 2010. "The Marquis de Condorcet goes to Bern," Public Choice, Springer, vol. 144(1), pages 119-131, July.
    17. 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.
    18. 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.
    19. Kurrild-Klitgaard, Peter, 2011. "Election inversions, coalitions and proportional representation: Examples from Danish elections," MPRA Paper 35302, University Library of Munich, Germany.

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