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Unanimity and the Anscombe’s Paradox

Author

Listed:
  • 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.

Suggested Citation

  • Gilbert Laffond & Jean Laine, 2013. "Unanimity and the Anscombe’s Paradox," Working Papers 201301, Murat Sertel Center for Advanced Economic Studies, Istanbul Bilgi University.
    • Handle: RePEc:msc:wpaper:201301
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    File URL: http://repeck.bilgi.org.tr/RePEc/msc/wpaper/mscenter_2013_12_AncombesParadox.pdf
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    References listed on IDEAS

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    1. Conal Duddy & Ashley Piggins, 2012. "A measure of distance between judgment sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 855-867, October.
    2. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521004046.
    3. 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.
    4. Wade D. Cook & Lawrence M. Seiford, 1978. "Priority Ranking and Consensus Formation," Management Science, INFORMS, vol. 24(16), pages 1721-1732, December.
    5. Steven Brams & D. Kilgour & M. Sanver, 2007. "A minimax procedure for electing committees," Public Choice, Springer, vol. 132(3), pages 401-420, September.
    6. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420, Decembrie.
    7. Saari,Donald G., 2001. "Decisions and Elections," Cambridge Books, Cambridge University Press, number 9780521808163.
    8. William V. Gehrlein & Dominique Lepelley, 2011. "Voting Paradoxes and Group Coherence," Studies in Choice and Welfare, Springer, number 978-3-642-03107-6, December.
    9. Laffond, G. & Laine, J., 2006. "Single-switch preferences and the Ostrogorski paradox," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 49-66, July.
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    Cited by:

    1. Gilbert Laffond & Jean Lainé, 2014. "Triple-consistent social choice and the majority rule," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 784-799, July.
    2. Hayrullah Dindar & Gilbert Laffond & Jean Laine, 2017. "The strong referendum paradox," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(4), pages 1707-1731, July.
    3. Nicolas Gabriel Andjiga & Issofa Moyouwou & Monge Kleber Kamdem Ouambo, 2017. "Avoiding Majority Dissatisfaction on a Series of Majority Decisions," Group Decision and Negotiation, Springer, vol. 26(3), pages 453-471, May.
    4. Hayrullah Dindar & Gilbert Laffond & Jean Lainé, 2021. "Referendum Paradox for Party-List Proportional Representation," Group Decision and Negotiation, Springer, vol. 30(1), pages 191-220, February.

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    More about this item

    Keywords

    Anscombe; Voting Paradox; Majority Rule; Unamity Issue-wise voting;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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