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Judgment aggregation: A critical view

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  • Danilov, V.

    (Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia)

Abstract

The paper gives a brief overview of the theory of aggregation. In theory and practice, one often has to deal with the problem of replacing a large array of homogeneous data with one number or item, which, to the greatest degree, represents this array. Mostly the situation is considered when data is aggregated issue-by-ussue. The main difficulty with this approach is that aggregation often leads to invalid (inconsistent) results. This means that the data to be aggregated, as well as the result of aggregation, must be connected by some specific restrictions. The classic example of this situation is the aggregation of preferences that are assumed to be transitive. Arrow's theorem speaks about the impossibility of maintaining the transitivity requirement under issue of preference aggregation. The culmination of this trend is the work of Nehring and Puppe, in which a complete description of the aggregation rules was obtained that do not lead to unacceptable results. Also, some generalizations related to multivalued questions, subject to aggregation, and the use of multivalued logic (MV-algebras) are discussed.

Suggested Citation

  • Danilov, V., 2024. "Judgment aggregation: A critical view," Journal of the New Economic Association, New Economic Association, vol. 65(4), pages 30-53.
    • Handle: RePEc:nea:journl:y:2024:i:65:p:30-53
    DOI: 10.31737/22212264_2024_4_30-53
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    References listed on IDEAS

    as
    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. Nehring, Klaus & Pivato, Marcus & Puppe, Clemens, 2014. "The Condorcet set: Majority voting over interconnected propositions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 268-303.
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    8. Klaus Nehring & Marcus Pivato, 2022. "The median rule in judgement aggregation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 1051-1100, June.
    9. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    median; filter; independence; MV-algebra; doctrinal paradox; unanimity; monotonicity; anonymity; dictatorship;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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