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Group decisions from individual rankings: The Borda–Condorcet rule

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  • Herrero, Carmen
  • Villar, Antonio

Abstract

This paper presents an evaluation protocol that transforms a collection of rankings, defined over a set of alternatives, into a complete, transitive, and cardinal assessment. It combines the ideas of Borda and Condorcet by computing the support that each alternative receives on average when confronted with any other. The protocol evaluates those alternatives in terms of pairwise comparisons but weighs the outcomes differently depending on how each alternative fares with respect to the others. The evaluation appears as the stable distribution of an iterative process in which each alternative competes randomly with any other, and results in a vector of positive numbers that tells us the relative support of the different options. We show that this protocol does not require linear orderings and can also be applied in the presence of incomplete rankings and when dealing with several issues simultaneously.

Suggested Citation

  • Herrero, Carmen & Villar, Antonio, 2021. "Group decisions from individual rankings: The Borda–Condorcet rule," European Journal of Operational Research, Elsevier, vol. 291(2), pages 757-765.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:2:p:757-765
    DOI: 10.1016/j.ejor.2020.09.043
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    References listed on IDEAS

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    1. Saaty, Thomas L., 2003. "Decision-making with the AHP: Why is the principal eigenvector necessary," European Journal of Operational Research, Elsevier, vol. 145(1), pages 85-91, February.
    2. Carmen Herrero & Antonio Villar, 2018. "The Balanced Worth: A Procedure to Evaluate Performance in Terms of Ordered Attributes," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 140(3), pages 1279-1300, December.
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    1. Antonio Villar, 2023. "Correction: The precedence function: a numerical evaluation method for multicriteria ranking problems," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 221-221, October.
    2. Antonio Villar, 2025. "Old rockers: Borda and Condorcet revisited," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(1), pages 45-53, April.
    3. Luis C. Dias & Humberto Rocha, 2023. "A stochastic method for exploiting outranking relations in multicriteria choice problems," Annals of Operations Research, Springer, vol. 321(1), pages 165-189, February.
    4. Carmen Herrero & Antonio Villar, 2022. "Sports competitions and the Break-Even rule," Working Papers 22.13, Universidad Pablo de Olavide, Department of Economics.
    5. Carmen Herrero & Antonio Villar, 2022. "Pairwise contests: wins, losses, and strength," Working Papers 22.11, Universidad Pablo de Olavide, Department of Economics.
    6. Atef Gharbi & Mohamed Ayari & Nasser Albalawi & Yamen El Touati & Zeineb Klai, 2025. "A Comparative Analysis of Fairness and Satisfaction in Multi-Agent Resource Allocation: Integrating Borda Count and K-Means Approaches with Distributive Justice Principles," Mathematics, MDPI, vol. 13(15), pages 1-18, July.
    7. Salvador Barberà & Walter Bossert, 2025. "A Characterization of Black's Voting Rule," Working Papers 1515, Barcelona School of Economics.
    8. Barberà, Salvador & Bossert, Walter, 2023. "Opinion aggregation: Borda and Condorcet revisited," Journal of Economic Theory, Elsevier, vol. 210(C).
    9. Pedro Albarrán & Carmen Herrero & Antonio Villar, 2024. "From people's preferences to political representation. The case of the Spanish regional elections," Working Papers 24.02, Universidad Pablo de Olavide, Department of Economics.
    10. Antonio Villar, 2023. "Old rockers," Working Papers 23.10, Universidad Pablo de Olavide, Department of Economics.

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