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Condorcet efficiency: Weighted Bucklin vs. weighted scoring and Borda

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  • Kilgour, D. Marc
  • Grégoire, Jean-Charles
  • Foley, Angèle M.

Abstract

We ask how good Bucklin-related procedures can be at identifying Condorcet winners in ranked-ballot, single-winner elections. Bucklin procedures can have a wide range of weighting vectors and thresholds; one, for example, applies Borda weights, analogous to the Borda Count in weighted scoring elections. Using simulation, we estimate the maximum Condorcet efficiency of both weighted Bucklin and weighted scoring elections as the number of voters becomes very large; these measures depend of course on the underlying distribution of ballots. For the impartial anonymous culture distribution, weighted Bucklin exhibits higher Condorcet efficiency than weighted scoring when there are 3 candidates, but is not as good when there are 4 candidates, and about equal when there are 5 or 6. We also compare them under the impartial culture distribution (equally good), and under a one-dimensional spatial model (weighted Bucklin is usually better, sometimes much better).

Suggested Citation

  • Kilgour, D. Marc & Grégoire, Jean-Charles & Foley, Angèle M., 2025. "Condorcet efficiency: Weighted Bucklin vs. weighted scoring and Borda," Mathematical Social Sciences, Elsevier, vol. 135(C).
    • Handle: RePEc:eee:matsoc:v:135:y:2025:i:c:s0165489625000356
    DOI: 10.1016/j.mathsocsci.2025.102420
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    References listed on IDEAS

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    1. Van Newenhizen, Jill, 1992. "The Borda Method Is Most Likely to Respect the Condorcet Principle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 69-83, January.
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    4. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2022. "Correction to: Weighted scoring elections: is Borda best?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 393-394, February.
    5. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2020. "The prevalence and consequences of ballot truncation in ranked-choice elections," Public Choice, Springer, vol. 184(1), pages 197-218, July.
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    13. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2022. "Weighted scoring elections: is Borda best?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 365-391, February.
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    Cited by:

    1. David McCune & Matthew I. Jones & Andy Schultz & Adam Graham-Squire & Ismar Volic & Belle See & Karen Xiao & Malavika Mukundan, 2026. "Candidate Moderation under Instant Runoff and Condorcet Voting: Evidence from the Cooperative Election Study," Papers 2603.03619, arXiv.org, revised Mar 2026.

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