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Unanimity and the Anscombe’s Paradox

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  • Gilbert Laffond

    ()
    (Laboratoire d'Econometrie, LIRSA)

  • Jean Laine

    ()
    (Murat Sertel Center for Advanced Economic Studies,Istanbul Bilgi University)

Abstract

We establish a new suffcient condition for avoiding a generalization of the Anscombe’s paradox. In a situation where ballots describe positions regarding finitely many yes-or-no issues, the Anscombe’s alpha−paradox holds if more than alpha % of the voters disagree with on a majority of issues with the outcome of issue-wise majority voting. We define the level of unanimity of a set of ballots as the number of issues minus the maximal symmetric diatance between two ballots. We compute for the caseof large electorates, the exact level of unanimity above which the Anscombe’s alpha−paradox never holds, whatever the distribution of votes among ballots.

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File URL: http://repeck.bilgi.edu.tr/RePEc/msc/wpaper/mscenter_2013_12_AncombesParadox.pdf
File Function: First version, 2013
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Bibliographic Info

Paper provided by Murat Sertel Center for Advanced Economic Studies, Istanbul Bilgi University in its series Working Papers with number 201301.

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Length: 17 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:msc:wpaper:201301

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Web page: http://mscenter.bilgi.edu.tr
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Related research

Keywords: Anscombe; Voting Paradox; Majority Rule; Unamity Issue-wise voting;

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  1. 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.
  2. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
  3. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
  4. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer, vol. 39(4), pages 855-867, October.
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