Theory and Decision

, Volume 71, Issue 2, pp 151–162 | Cite as

Condorcet vs. Borda in light of a dual majoritarian approach



Many voting rules and, in particular, the plurality rule and Condorcet-consistent voting rules satisfy the simple-majority decisiveness property. The problem implied by such decisiveness, namely, the universal disregard of the preferences of the minority, can be ameliorated by applying unbiased scoring rules such as the classical Borda rule, but such amelioration has a price; it implies erosion in the implementation of the widely accepted “majority principle”. Furthermore, the problems of majority decisiveness and of the erosion in the majority principle are not necessarily severe when one takes into account the likelihood of their occurrence. This paper focuses on the evaluation of the severity of the two problems, comparing simple-majoritarian voting rules that allow the decisiveness of the smallest majority larger than 1/2 and the classical Borda method of counts. Our analysis culminates in the derivation of the conditions that determine, in terms of the number of alternatives k, the number of voters n, and the relative (subjective) weight assigned to the severity of the two problems, which of these rules is superior in light of the dual majoritarian approach.


Majority decisiveness Condorcet criterion Erosion of majority principle The Borda method of counts 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baharad E., Nitzan S. (2002) Ameliorating majority decisiveness through expression of preference intensity. American Political Science Review 96(4): 745–754CrossRefGoogle Scholar
  2. Baharad E., Nitzan S. (2003) The Borda rule, Condorcet consistency and Condorcet stability. Economic Theory 22(3): 685–688CrossRefGoogle Scholar
  3. Baharad E., Nitzan S. (2007) The costs of implementing the majority principle: The golden voting rule. Economic Theory 31(1): 69–84CrossRefGoogle Scholar
  4. Brams, S. J., & Fishburn, P. C. (2002). Voting procedures. In K. Arrow, A. Sen, & K. Suzumura (Eds.), Handbook of social choice and welfare (Vol. I, Chap. 4, pp. 173–236) Amsterdam: Elsevier Science.Google Scholar
  5. Fishburn P.C. (1973) The theory of social choice. Princeton University Press, PrincetonGoogle Scholar
  6. Gehrlein W.V. (1983) Condorcet’s paradox. Theory and Decision 15: 161–197CrossRefGoogle Scholar
  7. Gehrlein W.V., Fishburn P.C. (1976) The probability of paradox of voting: A computable solution. Journal of Economic Theory 13: 14–25CrossRefGoogle Scholar
  8. Gehrlein W.V., Lepelley D. (1998) The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser. Journal of Mathematical Economics 29(3): 271–283CrossRefGoogle Scholar
  9. Lepelley D., Merlin V. (2001) Scoring run-off paradoxes for variable electorates. Economic Theory 17(1): 53–80CrossRefGoogle Scholar
  10. Merlin V., Tataru M., Valognes F. (2002) On the likelihood of Condorcet’s profiles. Social Choice and Welfare 19(1): 193–206CrossRefGoogle Scholar
  11. Merrill S. III. (1984) A comparison of efficiency of multi-candidate elections systems. American Journal of Political Science 28: 23–48CrossRefGoogle Scholar
  12. Mueller, D. C. (2003). Public choice III. Cambridge University Press.Google Scholar
  13. Nurmi H. (1999) Voting paradoxes and how to deal with them. Springer-Verlag, Berlin, Heidelberg, New YorkGoogle Scholar
  14. Nurmi H. (2002) Voting procedures under uncertainty. Springer-Verlag, Berlin, Heidelberg, New YorkGoogle Scholar
  15. Nurmi H., Uusi-Heikkila Y. (1986) Computer simulations of approval and plurality voting. European Journal of Political Economy 2: 54–78Google Scholar
  16. Saari D.G. (1990) The Borda dictionary. Social Choice and Welfare 7: 279–317CrossRefGoogle Scholar
  17. Saari D.G. (1995) Basic geometry of voting. Springer, BerlinCrossRefGoogle Scholar
  18. Saari, D. G. (2001). Chaotic elections! A mathematician looks at voting. American Mathematical Society, Providence.Google Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of HaifaHaifaIsrael
  2. 2.Department of EconomicsBar Ilan UniversityRamat GanIsrael

Personalised recommendations