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Weighted scoring elections: is Borda best?

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A Correction to this article was published on 26 November 2021

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Abstract

Weighted scoring rules, perhaps the most common procedures for multi-candidate, single-winner elections, are defined by score vectors, of which the Borda Count is the best known example. The concept of Borda dominance identifies candidates who cannot win under any score vector; we assess its usefulness in the context of single-winner elections. We propose several families of score vectors that can accommodate any number of candidates, asking whether any of them can improve on Borda Count. Using large-scale simulation, we compare score vectors on Condorcet efficiency, or ability to find a Condorcet winner when one exists, on resilience to ballot truncation, and on ability to maximize the Copeland score using both complete and uniformly truncated ballots. Borda performs well on criteria related to Condorcet winner and Copeland score but, depending on the preference model, may not be optimal. Convex score vectors are the most resilient to ballot truncation.

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Acknowledgements

The authors thank two anonymous referees for extensive and insightful comments that helped us to improve the paper. This work was supported by the Canadian Tri-Council Research Support Fund, specifically by the authors’ individual Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants.

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Authors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    D. Marc Kilgour & Angèle M. Foley

  2. Institut National de la Recherche Scientifique, Montréal, QC, H5A 1K6, Canada

    Jean-Charles Grégoire

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  1. D. Marc Kilgour
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  2. Jean-Charles Grégoire
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  3. Angèle M. Foley
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Correspondence to D. Marc Kilgour.

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The original online version of this article was revised due to incorrect Tables 5 and 7. Now, they have been corrected.

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Kilgour, D.M., Grégoire, JC. & Foley, A.M. Weighted scoring elections: is Borda best?. Soc Choice Welf 58, 365–391 (2022). https://doi.org/10.1007/s00355-021-01347-6

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