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Borda and Condorcet: Some Distance Results

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  • Christian Klamler

Abstract

This paper provides a distance based analysis of the Borda rule with respect to Condorcet’s criterion. It shows that the minimal Condorcet consistency present in the Borda rule, whenever a Condorcet winner (the alternative that wins against every other alternative in a pairwise contest) exists, disappears in the case of voting cycles. First, it is shown that for certain preference profiles the Borda winner is furthest from being a Condorcet winner. Second, it is shown that there exist preference profiles for which the Borda winner is closest from being a Condorcet loser (the alternative that loses against every other alternative in a pairwise contest). Copyright Springer 2005

Suggested Citation

  • Christian Klamler, 2005. "Borda and Condorcet: Some Distance Results," Theory and Decision, Springer, vol. 59(2), pages 97-109, September.
    • Handle: RePEc:kap:theord:v:59:y:2005:i:2:p:97-109
    DOI: 10.1007/s11238-005-5459-y
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    Citations

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    Cited by:

    1. Christian Klamler, 2005. "On the Closeness Aspect of Three Voting Rules: Borda – Copeland – Maximin," Group Decision and Negotiation, Springer, vol. 14(3), pages 233-240, May.
    2. Edith Elkind & Piotr Faliszewski & Arkadii Slinko, 2012. "Rationalizations of Condorcet-consistent rules via distances of hamming type," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 891-905, October.
    3. Andreas Darmann & Julia Grundner & Christian Klamler, 2017. "Consensus in the 2015 Provincial Parliament Election in Styria, Austria: Voting Rules,Outcomes, and the Condorcet Paradox," Graz Economics Papers 2017-13, University of Graz, Department of Economics.
    4. Emilio De Santis & Fabio Spizzichino, 2023. "Construction of voting situations concordant with ranking patterns," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 129-156, June.
    5. Eduardo Fernandez & Sergio Bernal & Jorge Navarro & Rafael Olmedo, 2010. "An outranking-based fuzzy logic model for collaborative group preferences," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 444-464, December.
    6. Darmann, Andreas & Grundner, Julia & Klamler, Christian, 2019. "Evaluative voting or classical voting rules: Does it make a difference? Empirical evidence for consensus among voting rules," European Journal of Political Economy, Elsevier, vol. 59(C), pages 345-353.
    7. Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(4), pages 575-601, May.

    More about this item

    Keywords

    voting cycles; Borda rule; distance functions; Condorcet winner; Condorcet loser; D70;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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