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Unanimity and the Anscombe’s paradox

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  • G. Laffond
  • J. Lainé

Abstract

We establish a new sufficient condition for avoiding a generalized Anscombe’s paradox. In a situation where votes describe positions regarding finitely many yes-or-no issues, the Anscombe’s α-paradox holds if more than α% of the voters disagree on a majority of issues with the outcome of issue-wise majority voting. We define the level of unanimity of a set of votes as the number of issues minus the maximal Hamming distance between two votes. We compute for the case of large electorates the exact level of unanimity above which the Anscombe’s α-paradox never holds, whatever the distribution of individuals among votes. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • G. Laffond & J. Lainé, 2013. "Unanimity and the Anscombe’s paradox," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 590-611, October.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:3:p:590-611
    DOI: 10.1007/s11750-011-0192-x
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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; Unanimity; Issue-wise voting; 91B12;
    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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