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A Representation Theorem For Voting With Logical Consequences

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  • GÄRDENFORS, PETER

Abstract

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem.

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  • Gärdenfors, Peter, 2006. "A Representation Theorem For Voting With Logical Consequences," Economics and Philosophy, Cambridge University Press, vol. 22(2), pages 181-190, July.
    • Handle: RePEc:cup:ecnphi:v:22:y:2006:i:02:p:181-190_00
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    Cited by:

    1. Christian List, 2007. "Group deliberation and the transformation ofjudgments: an impossibility result," STICERD - Political Economy and Public Policy Paper Series 26, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Herzberg, Frederik S., 2008. "Judgement aggregation functions and ultraproducts," MPRA Paper 10546, University Library of Munich, Germany, revised 10 Sep 2008.
    3. Minkyung Wang, 2024. "Aggregating individual credences into collective binary beliefs: an impossibility result," Theory and Decision, Springer, vol. 97(1), pages 39-66, August.
    4. Aureli Alabert & Mercè Farré & Rubén Montes, 2023. "Optimal Decision Rules for the Discursive Dilemma," Group Decision and Negotiation, Springer, vol. 32(4), pages 889-923, August.
    5. Marcel Heidemann, 2018. "Judgment aggregation and minimal change: a model of consensus formation by belief revision," Theory and Decision, Springer, vol. 85(1), pages 61-97, July.
    6. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    7. Pivato, Marcus, 2008. "The Discursive Dilemma and Probabilistic Judgement Aggregation," MPRA Paper 8412, University Library of Munich, Germany.
    8. Zoi Terzopoulou & Ulle Endriss, 2019. "Strategyproof judgment aggregation under partial information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 415-442, October.
    9. Terzopoulou, Zoi, 2020. "Quota rules for incomplete judgments," Mathematical Social Sciences, Elsevier, vol. 107(C), pages 23-36.
    10. Beg, Ismat & Syed, Ayesha, 2016. "An interactive fuzzy judgment aggregation model for consensus with partially undecided judges," MPRA Paper 96096, University Library of Munich, Germany, revised 14 Apr 2017.

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