Public Choice

, Volume 107, Issue 1–2, pp 135–145

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

  • Peter Kurrild-Klitgaard


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arrow, K.J. (1951). Social choice and individual values, 2nd rev. edn. New Haven: Yale University Press, 1963.Google Scholar
  2. Black, D. (1958). The theory of committees and elections, 2nd rev. edn. Dordrecht: Kluwer, 1998.Google Scholar
  3. Blydenburgh, J.C. (1971). The closed rule and the paradox of voting. Journal of Politics 33: 57-71.CrossRefGoogle Scholar
  4. Borre, O., and Andersen, J.G. (1997). Voting and political attitudes in Denmark: A study of the 1994 election. Aarhus: Aarhus University Press.Google Scholar
  5. Campbell, C. and Tullock, G. (1965). A measure of the importance of cyclical majorities. Economic Journal 75: 853-857.CrossRefGoogle Scholar
  6. Chamberlain, J.R., Cohen, J.L. and Coombs, C.H. (1984). Social choice observed: Five presidential elections of the American Psychological Association. Journal of Politics 46: 479-502.CrossRefGoogle Scholar
  7. DeMeyer, F. and Plott, C.R. (1970). The probability of a cyclical majority. Econometrica 38: 345-354.CrossRefGoogle Scholar
  8. Dobra, J.L. (1983). An approach to empirical studies of voting paradoxes: An update and extension. Public Choice 41: 241-250.CrossRefGoogle Scholar
  9. Downs, A. (1957). An economic theory of democracy. New York: Harper and Row.Google Scholar
  10. Feld, S.L. and Grofman, B. (1992): Who's afraid of the Big Bad Cycle? Evidence from 36 elections. Journal of Theoretical Politics 4: 231-237.Google Scholar
  11. Garman, M.B. and Kamien, M.I. (1968). The paradox of voting: Probability calculations. Behavioral Science 13: 306-316.Google Scholar
  12. Gehrlein, W.V. (1983). Condorcet's paradox. Theory and Decision 15: 161-197.CrossRefGoogle Scholar
  13. Gehrlein, W.V. and Fishburn, P.C. (1976). The probability of the paradox of voting: A computable solution. Journal of Economic Theory 13: 14-25.CrossRefGoogle Scholar
  14. Jamison, D.T. (1975). The probability of intransitive majority rule: An empirical study. Public Choice 23: 87-94.CrossRefGoogle Scholar
  15. Jones, B., Radcliff, B., Taber, C. and Timpone, R. (1995). Condorcet winners and the paradox of voting: Probability calculations for weak preference orders. American Political Science Review 89: 137-147.CrossRefGoogle Scholar
  16. Klahr, D. (1966). A computer simulation of the paradox of voting. American Political Science Review 60: 384-390.CrossRefGoogle Scholar
  17. Kurrild-Klitgaard, P. (1996). Magt, demokrati og kollektive valgs rationalitet, AP 1996/4. København: Institut for Statskundskab. In U. Jakobsen and M. Kelstrup (Eds.), Demokrati: Teorier og Begreber. Copenhagen: Political Studies Press, forthcoming 1999.Google Scholar
  18. Lagerspaetz, E. (1993). Social choice in the real world. Scandinavian Political Studies 16: 1-23.Google Scholar
  19. Lagerspaetz, E. (1997). Social choice in the real world II: Cyclical preferences and strategic voting in the Finnish presidential elections. Scandinavian Political Studies 20: 53-67.Google Scholar
  20. Lewin, L. (1996). Votera eller Förhandla? Om Den Svenska Parlamentarismen. Stockholm: Fritzes.Google Scholar
  21. Lewin, L. (1998). Majoritarian and consensus democracy: The Swedish experience. Scandinavian Political Studies 21: 195-206.Google Scholar
  22. Niemi, R.G. (1970). The occurrence of the paradox of voting in university elections. Public Choice 8: 91-100.CrossRefGoogle Scholar
  23. Niemi, R.G. and Weisberg, H.F. (1968). A mathematical solution for the probability of the paradox of voting. Behavioral Science 13: 317-323Google Scholar
  24. Niemi, R.G. and Wright, S. (1987). Voting cycles and the structure of individual preferences. Social Choice and Welfare 4: 173-183.CrossRefGoogle Scholar
  25. Plott, C.R. (1976). Axiomatic social choice theory: An overview and interpretation. American Journal of Political Science 20: 511-596.Google Scholar
  26. Radcliff, B. (1994). Collective preferences in presidential elections. Electoral Studies 13: 50-57.CrossRefGoogle Scholar
  27. Riker, W.H. (1958). The paradox of voting and congressional rules for voting on amendments. American Political Science Review 52: 349-366.CrossRefGoogle Scholar
  28. Riker, W.H. (1965). Arrow's Theorem and some examples of the paradox of voting. In J.M. Claunch (Ed.), Mathematical applications in political science, Vol. I. Dallas: Southern Methodist University Press: 41-60.Google Scholar
  29. Riker, W.H. (1982). Liberalism against populism: A confrontation between the theory of democracy and the theory of social choice. Prospect Heights: Waveland Press.Google Scholar
  30. Riker, W.H. (1986). The art of manipulation. New Haven: Yale University Press.Google Scholar
  31. Shepsle, K.A. (1979). Institutional arrangements and equilibrium in multidimensional voting models. American Journal of Political Science 23: 27-59.Google Scholar
  32. Shepsle, K.A. and Weingast, B.R. (1981). Structure-induced equilibrium and legislative choice. Public Choice 37: 503-519.CrossRefGoogle Scholar
  33. Tullock, G. (1967). Toward a mathematics of politics. Ann Arbor: University of Michigan Press.Google Scholar
  34. Tullock, G. (1981). Why so much stability? Public Choice 37: 189-202.CrossRefGoogle Scholar
  35. Van Deemen., A.M.A. (1998a). The probability of the paradox of voting for weak preference orderings. Social Choice and Welfare forthcoming.Google Scholar
  36. Van Deemen, A.M.A. (1998b). The Condorcet paradox: A review of research results. Paper presented at the Workshop on Empirical Social Choice, ECPR Joint Sessions, Warwick, March 23-28, 1998.Google Scholar
  37. Van Deemen, A.M.A. and Vergunst, N.P. (1998). Empirical evidence of paradoxes of voting in Dutch elections. Public Choice 97: 475-490.CrossRefGoogle Scholar
  38. Van den Doel, H. (1979). Democracy and welfare economics. Cambridge: Cambridge University Press.Google Scholar
  39. Vergunst, N.P. (1996). Besluitvorming over kerncentrale Borssele: Een analyse van de stemparadox in de Nederlandse politiek. Acta Politica 31: 209-228.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Peter Kurrild-Klitgaard
    • 1
  1. 1.Department of Political ScienceUniversity of AarhusAarhus CDenmark

Personalised recommendations