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Distance rationalization of voting rules

Listed author(s):
  • Edith Elkind

    ()

  • Piotr Faliszewski
  • Arkadii Slinko
Registered author(s):

    The concept of distance rationalizability allows one to define new voting rules or rationalize existing ones via a consensus, i.e., a class of elections that have a unique, indisputable winner, and a distance over elections: A candidate is declared an election winner if she is the consensus candidate in one of the nearest consensus elections. Many classic voting rules are defined or can be represented in this way. In this paper, we focus on the power and the limitations of the distance rationalizability approach. Lerer and Nitzan (J Econ Theory 37(1):191–201, 1985 ) and Campbell and Nitzan (Soc Choice Welf 3(1):1–16, 1986 ) show that if we do not place any restrictions on the notions of distance and consensus then essentially all voting rules can be distance-rationalized. We identify a natural class of distances on elections—votewise distances—which depend on the submitted votes in a simple and transparent manner, and investigate which voting rules can be rationalized via distances of this type. We also study axiomatic properties of rules that can be defined via votewise distances. Copyright Springer-Verlag Berlin Heidelberg 2015

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    File URL: http://hdl.handle.net/10.1007/s00355-015-0892-5
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    Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

    Volume (Year): 45 (2015)
    Issue (Month): 2 (September)
    Pages: 345-377

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    Handle: RePEc:spr:sochwe:v:45:y:2015:i:2:p:345-377
    DOI: 10.1007/s00355-015-0892-5
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    1. Young, H. P., 1977. "Extending Condorcet's rule," Journal of Economic Theory, Elsevier, vol. 16(2), pages 335-353, December.
    2. Wade D. Cook & Lawrence M. Seiford, 1982. "On the Borda-Kendall Consensus Method for Priority Ranking Problems," Management Science, INFORMS, vol. 28(6), pages 621-637, June.
    3. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
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    10. 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.
    11. Fuad Aleskerov & Vyacheslav Chistyakov & Valery Kalyagin, 2010. "Social threshold aggregations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 627-646, October.
    12. Aleskerov, Fuad & Chistyakov, Vyacheslav V. & Kalyagin, Valery, 2010. "The threshold aggregation," Economics Letters, Elsevier, vol. 107(2), pages 261-262, May.
    13. Nick Baigent & Christian Klamler, 2003. "Transitive closure, proximity and intransitivities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 175-181, December.
    14. 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.
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