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Condorcet-loser dominance among scoring rules

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  • Ryoga Doi
  • Kensei Nakamura

Abstract

This paper studies a dominance relation among scoring rules with respect to avoiding the selection of the Condorcet loser. In a voting model with three or more alternatives, we say that a scoring rule $f$ Condorcet-loser-dominates (CL-dominates) another scoring rule $g$ if the set of profiles where $f$ selects a Condorcet loser is a proper subset of the set where $g$ does. We show that the Borda rule not only CL-dominates all other scoring rules, but also is the only scoring rule that CL-dominates some scoring rule.

Suggested Citation

  • Ryoga Doi & Kensei Nakamura, 2026. "Condorcet-loser dominance among scoring rules," Papers 2604.05916, arXiv.org.
    • Handle: RePEc:arx:papers:2604.05916
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    References listed on IDEAS

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    1. Battal Doğan & Lars Ehlers, 2022. "Robust Minimal Instability of the Top Trading Cycles Mechanism," American Economic Journal: Microeconomics, American Economic Association, vol. 14(4), pages 556-582, November.
    2. Doi, Ryoga & Okamoto, Noriaki, 2024. "Condorcet-loser dominance between the plurality rule and other scoring rules," Economics Letters, Elsevier, vol. 237(C).
    3. Saari, Donald G., 1989. "A dictionary for voting paradoxes," Journal of Economic Theory, Elsevier, vol. 48(2), pages 443-475, August.
    4. Noriaki Okamoto & Toyotaka Sakai, 2019. "The Borda rule and the pairwise-majority-loser revisited," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 75-89, June.
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