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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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    Cited by:

    1. 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.
    2. Carmen Herrero & Antonio Villar, 2022. "Sports competitions and the Break-Even rule," Working Papers 22.13, Universidad Pablo de Olavide, Department of Economics.
    3. Carmen Herrero & Antonio Villar, 2022. "Pairwise contests: wins, losses, and strength," Working Papers 22.11, Universidad Pablo de Olavide, Department of Economics.
    4. Barberà, Salvador & Bossert, Walter, 2023. "Opinion aggregation: Borda and Condorcet revisited," Journal of Economic Theory, Elsevier, vol. 210(C).
    5. 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.
    6. Antonio Villar, 2023. "Old rockers," Working Papers 23.10, Universidad Pablo de Olavide, Department of Economics.

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