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Characterizing the Borda ranking rule for a fixed population

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  • Mihara, H. Reiju

Abstract

A ranking rule (social welfare function) for a fixed population assigns a social preference to each profile of preferences. The rule satisfies "Positional Cancellation" if changes in the relative positions of two alternatives that cancel each other do not alter the social preference between the two. I show that the Borda rule is the only ranking rule that satisfies "Reversal" (a weakening of neutrality), "Positive Responsiveness," and "Pairwise Cancellation."

Suggested Citation

  • Mihara, H. Reiju, 2017. "Characterizing the Borda ranking rule for a fixed population," MPRA Paper 78093, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:78093
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    References listed on IDEAS

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    1. H. Reiju Mihara, 1997. "Arrow's Theorem and Turing computability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 257-276.
    2. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
    3. Kumabe, Masahiro & Mihara, H. Reiju, 2011. "Preference aggregation theory without acyclicity: The core without majority dissatisfaction," Games and Economic Behavior, Elsevier, vol. 72(1), pages 187-201, May.
    4. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    5. Shmuel Nitzan & Ariel Rubinstein, 1981. "A further characterization of Borda ranking method," Public Choice, Springer, vol. 36(1), pages 153-158, January.
    6. Pattanaik, Prasanta K., 2002. "Positional rules of collective decision-making," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 7, pages 361-394, Elsevier.
    7. Peter Fishburn & William Gehrlein, 1976. "Borda's rule, positional voting, and Condorcet's simple majority principle," Public Choice, Springer, vol. 28(1), pages 79-88, December.
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    Cited by:

    1. 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.
    2. Wesley H. Holliday & Eric Pacuit, 2020. "Axioms for Defeat in Democratic Elections," Papers 2008.08451, arXiv.org, revised Oct 2023.
    3. Hans Gersbach & Rodrigo Casado Noguerales & Samuel Schenk, 2024. "A Better Cycle-Breaker for Swiss Democracy?," CESifo Working Paper Series 11265, CESifo.
    4. Yifeng Ding & Wesley H. Holliday & Eric Pacuit, 2022. "An Axiomatic Characterization of Split Cycle," Papers 2210.12503, arXiv.org, revised Jun 2024.
    5. Kelly, Jerry S. & Qi, Shaofang, 2019. "Balancedness of social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 59-67.
    6. Guy Barokas & Yves Sprumont, 2022. "The broken Borda rule and other refinements of approval ranking," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(1), pages 187-199, January.
    7. Antonio Villar, 2023. "Old rockers," Working Papers 23.10, Universidad Pablo de Olavide, Department of Economics.

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    More about this item

    Keywords

    Borda rule; Borda count; scoring rules; positional rules; axiomatic characterization;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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