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Rationalizations of Condorcet-consistent rules via distances of hamming type


  • Edith Elkind


  • Piotr Faliszewski


  • Arkadii Slinko



In voting, the main idea of the distance rationalizability framework is to view the voters’ preferences as an imperfect approximation to some kind of consensus. This approach, which is deeply rooted in the social choice literature, allows one to define (“rationalize”) voting rules via a consensus class of elections and a distance: a candidate is said to be an election winner if she is ranked first in one of the nearest (with respect to the given distance) consensus elections. It is known that many classic voting rules can be distance-rationalized. In this article, we provide new results on distance rationalizability of several Condorcet-consistent voting rules. In particular, we distance-rationalize the Young rule and Maximin using distances similar to the Hamming distance. It has been claimed that the Young rule can be rationalized by the Condorcet consensus class and the Hamming distance; we show that this claim is incorrect and, in fact, this consensus class and distance yield a new rule, which has not been studied before. We prove that, similarly to the Young rule, this new rule has a computationally hard winner determination problem. Copyright Springer-Verlag 2012

Suggested Citation

  • 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.
  • Handle: RePEc:spr:sochwe:v:39:y:2012:i:4:p:891-905
    DOI: 10.1007/s00355-011-0555-0

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    References listed on IDEAS

    1. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
    2. Christian Klamler, 2005. "Borda and Condorcet: Some Distance Results," Theory and Decision, Springer, vol. 59(2), pages 97-109, September.
    3. Baigent, Nick, 1987. "Metric rationalisation of social choice functions according to principles of social choice," Mathematical Social Sciences, Elsevier, vol. 13(1), pages 59-65, February.
    4. Christian Klamler, 2005. "The Copeland rule and Condorcet’s principle," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 745-749, April.
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    Cited by:

    1. Can, B., 2013. "Distance rationalizability of scoring rules," Research Memorandum 068, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Bredereck, Robert & Chen, Jiehua & Woeginger, Gerhard J., 2016. "Are there any nicely structured preference profiles nearby?," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 61-73.

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