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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. 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.
    2. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    3. Herzberg, Frederik S., 2008. "Judgement aggregation functions and ultraproducts," MPRA Paper 10546, University Library of Munich, Germany, revised 10 Sep 2008.
    4. Terzopoulou, Zoi, 2020. "Quota rules for incomplete judgments," Mathematical Social Sciences, Elsevier, vol. 107(C), pages 23-36.
    5. Pivato, Marcus, 2008. "The Discursive Dilemma and Probabilistic Judgement Aggregation," MPRA Paper 8412, University Library of Munich, Germany.
    6. 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.
    7. 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.
    8. Minkyung Wang, 2024. "Aggregating individual credences into collective binary beliefs: an impossibility result," Theory and Decision, Springer, vol. 97(1), pages 39-66, August.
    9. List, Christian, 2007. "Group deliberation and the transformation of judgments: an impossibility result," LSE Research Online Documents on Economics 19273, London School of Economics and Political Science, LSE Library.
    10. 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.

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