Two-Stage Election Procedures

  • William V. Gehrlein
  • Dominique Lepelley
Part of the Studies in Choice and Welfare book series (WELFARE)


The standard two-stage voting rules Plurality Elimination and Negative Plurality Elimination are evaluated relative to Borda Rule on the basis of Condorcet Efficiency. Theoretical analysis shows that the Condorcet Efficiency of these two-stage voting rules consistently marginally dominate Borda Rule as the various measures of group mutual coherence change. However, it is also found that the probability that either of the two-stage rules will elect a different candidate than the winner by Borda Rule is quite small. Empirically-based analysis reinforces this observation to lead to the general conclusion that the additional effort that is required to use a two-stage voting rule, rather than simply using Borda Rule, is not likely to be worthwhile. Other benefits are considered that result from using Borda Rule rather than a two-stage voting rule.


  1. Black, D. (1958). The theory of committees and elections. Cambridge: Cambridge University Press.Google Scholar
  2. de Condorcet, M. (1788a). On discovering the plurality will in an election. In I. McLean & F. Hewitt (Eds.), Condorcet: Foundations of social choice and political theory (pp. 148–156). Hants: Edward Elgar.Google Scholar
  3. de Condorcet, M. (1788b). On the form of elections. In I. McLean & F. Hewitt (Eds.), Condorcet: Foundations of social choice and political theory (pp. 139–147). Hants: Edward Elgar.Google Scholar
  4. de Condorcet, M. (1789). On the form of elections. In I. McLean & F. Hewitt (Eds.), Condorcet: Foundations of social choice and political theory (pp. 169–189). Hants: Edward Elgar.Google Scholar
  5. Fishburn, P. C., & Gehrlein, W. V. (1976). Borda’s rule, positional voting, and Condorcet’s simple majority principle. Public Choice, 28, 79–88.CrossRefGoogle Scholar
  6. Gehrlein, W. V., & Lepelley, D. (2011). Voting paradoxes and group coherence: The Condorcet efficiency of voting rules. Berlin: Springer.CrossRefGoogle Scholar
  7. Gehrlein, W. V., & Lepelley, D. (2016). Refining measures of group mutual coherence. Quality and Quantity, 50, 1845–1870.CrossRefGoogle Scholar
  8. Gehrlein, W. V., & Plassmann, F. (2014). A comparison of theoretical and empirical evaluations of the Borda Compromise. Social Choice and Welfare, 43, 747–772.CrossRefGoogle Scholar
  9. Gehrlein, W. V., Lepelley, D., & Smaoui, H. (2011). The Condorcet efficiency of voting rules with mutually coherent voter preferences: A Borda compromise. Annals of Economics and Statistics, 101/102, 107–125.CrossRefGoogle Scholar
  10. Gehrlein, W. V., Lepelley, D., & Plassmann, F. (2017, forthcoming). An evaluation of the benefit of using two-stage election procedures. Homo Oeconomicus.Google Scholar
  11. Lepelley, D., Moyouwou, I., & Samoui, H. (2015). Monotonicity paradoxes in three-candidate elections using scoring elimination rules. Social Choice and Welfare. doi: 10.13140/RG.2.1.5075.4961.
  12. Miller, N. R. (2016). Monotonicity failure in IRV elections with three candidates: Closeness matters. Working paper. Available at
  13. Saari, D. G. (1989). A dictionary for voter paradoxes. Journal of Economic Theory, 48, 443–475.CrossRefGoogle Scholar
  14. Saari, D. G. (1990). The Borda dictionary. Social Choice and Welfare, 7, 279–317.CrossRefGoogle Scholar
  15. Saari, D. G. (1996). The mathematical symmetry of choosing. Mathematica Japonica, 44, 183–200.Google Scholar
  16. Saari, D. G. (1999). Explaining all three-alternative voting outcomes. Journal of Economic Theory, 87, 313–355.CrossRefGoogle Scholar
  17. Santucci, J. (2016, October 13). Will ranked-choice voting succeed in Maine? That depends on the Democrats. Washington Post. Available at
  18. Seelye, K. Q. (2016, December 3). Maine adopts ranked-choice voting: What is it and how will it work. New York Times. Available at
  19. Wright, S. G., & Riker, W. H. (1989). Plurality and runoff systems and numbers of candidates. Public Choice, 60, 155–175.CrossRefGoogle Scholar
  20. Young, H. P. (1974). An axiomatization of Borda rule. Journal of Economic Theory, 9, 43–52.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • William V. Gehrlein
    • 1
  • Dominique Lepelley
    • 2
  1. 1.Department of Business AdministrationUniversity of DelawareNewarkUSA
  2. 2.University of La RéunionSaint-Denis, Ile de La RéunionFrance

Personalised recommendations