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Old rockers: Borda and Condorcet revisited

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  • Antonio Villar

    (Universidad Pablo de Olavide)

Abstract

This paper explores the relationship between two classic social evaluation procedures: the Borda count, and (an extension of) the Condorcet criterion. We provide a straightforward way of identifying and comparing those evaluation protocols, dispensing with the transitivity of individual preferences. Our approach uses individual pairwise comparisons of alternatives as informational inputs, with complete social orderings as informational outputs. We show that, keeping Arrow’s framework but weakening the property of independence of irrelevant alternatives to independence of separate pairs (the evaluation of each alternative only depends on how people compare this alternative with each other), opens the door to Borda and Condorcet evaluation functions. The key difference between these two protocols is the type of monotonicity assumed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:etbull:v:13:y:2025:i:1:d:10.1007_s40505-024-00279-5
    DOI: 10.1007/s40505-024-00279-5
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    References listed on IDEAS

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    1. Shmuel Nitzan & Ariel Rubinstein, 1981. "A further characterization of Borda ranking method," Public Choice, Springer, vol. 36(1), pages 153-158, January.
    2. Claude D'Aspremont & Louis Gevers, 1977. "Equity and the Informational Basis of Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 199-209.
    3. Partha Dasgupta & Eric Maskin, 2020. "Strategy-Proofness, Independence of Irrelevant Alternatives, and Majority Rule," American Economic Review: Insights, American Economic Association, vol. 2(4), pages 459-474, December.
    4. Merlin, Vincent R. & Saari, Donald G., 1997. "Copeland Method II: Manipulation, Monotonicity, and Paradoxes," Journal of Economic Theory, Elsevier, vol. 72(1), pages 148-172, January.
    5. Antonio Villar, 2023. "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 211-219, October.
    6. Mihara, H. Reiju, 2017. "Characterizing the Borda ranking rule for a fixed population," MPRA Paper 78093, University Library of Munich, Germany.
    7. Partha Dasgupta & Eric Maskin, 2008. "On The Robustness of Majority Rule," Journal of the European Economic Association, MIT Press, vol. 6(5), pages 949-973, September.
    8. Young, H. P., 1988. "Condorcet's Theory of Voting," American Political Science Review, Cambridge University Press, vol. 82(4), pages 1231-1244, December.
    9. 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.
    10. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Independence of irrelevant alternatives; Borda count; Condorcet evaluation function; Independence of separate pairs; Individual and pivotal monotonicity; Substitutability;
    All these keywords.

    JEL classification:

    • D60 - Microeconomics - - Welfare Economics - - - General
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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