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Condorcet efficiency: A preference for indifference


  • Fabrice Valognes

    () (University of Namur, Department of Economics, B-5000 Namur, Belgium)

  • William V. Gehrlein

    () (University of Delaware, Department of Business Administration, Newark, DE 19716, USA)


The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet winner, given that a Condorcet winner exists. The study considers the Condorcet efficiency of weighted scoring rules (WSR's) on three candidates for large electorates when voter indifference between candidates is allowed. It is shown that increasing the proportion of voters who have partial indifference will increase the probability that a Condorcet winner exists, and will also increase the Condorcet efficiency of all WSR's. The same observation is observed when the proportion of voters with complete preferences on candidates is reduced. Borda Rule is shown to be the WSR with maximum Condorcet efficiency over a broad range of assumptions related to voter preferences. The result of forcing voters to completely rank all candidates, by randomly breaking ties on candidates that are viewed as indifferent, leads to a reduction in the probability that a Condorcet winner exists and to a reduction in the Condorcet efficiency of all WSR's.

Suggested Citation

  • Fabrice Valognes & William V. Gehrlein, 2001. "Condorcet efficiency: A preference for indifference," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 193-205.
  • Handle: RePEc:spr:sochwe:v:18:y:2001:i:1:p:193-205
    Note: Received: 31 July 1999/Accepted: 11 February 2000

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    References listed on IDEAS

    1. Donald E. Campbell & Jerry S. Kelly, 2006. "Social Welfare Functions that Satisfy Pareto, Anonymity, and Neutrality: Countable Many Alternatives," Working Papers 43, Department of Economics, College of William and Mary.
    2. Campbell, Donald E. & Kelly, Jerry S., 2002. "Impossibility theorems in the arrovian framework," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 1, pages 35-94 Elsevier.
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    Cited by:

    1. Mostapha Diss & Vincent Merlin, 2010. "On the stability of a triplet of scoring rules," Theory and Decision, Springer, vol. 69(2), pages 289-316, August.
    2. 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.
    3. repec:spr:qualqt:v:51:y:2017:i:6:d:10.1007_s11135-016-0446-7 is not listed on IDEAS
    4. Regenwetter, Michel & Grofman, Bernard & Marley, A. A. J., 2002. "On the model dependence of majority preference relations reconstructed from ballot or survey data," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 451-466, July.
    5. Mathieu Martin, 2002. "On the emptiness of the stability set of order d," Theory and Decision, Springer, vol. 52(4), pages 313-326, June.
    6. Hervé Crès, 2000. "Aggregation of Coarse Preferences," Working Papers hal-01064879, HAL.
    7. 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.
    8. repec:spr:grdene:v:24:y:2015:i:2:d:10.1007_s10726-014-9388-4 is not listed on IDEAS
    9. William V. Gehrlein & Dominique Lepelley, 2015. "The Condorcet Efficiency Advantage that Voter Indifference Gives to Approval Voting Over Some Other Voting Rules," Group Decision and Negotiation, Springer, vol. 24(2), pages 243-269, March.
    10. 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.
    11. Hervé Crès, 2000. "Aggregation of Coarse Preferences," Sciences Po publications 659/1998, Sciences Po.
    12. 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.

    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations


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