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Judgment aggregation: A critical view

Author

Listed:
  • 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. Nehring, Klaus & Puppe, Clemens, 2010. "Abstract Arrowian aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 467-494, March.
    2. 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.
    3. 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.
    4. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    5. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
    6. Wilson, Robert, 1975. "On the theory of aggregation," Journal of Economic Theory, Elsevier, vol. 10(1), pages 89-99, February.
    7. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    8. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    9. 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.
    10. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    11. Chichilnisky, Graciela & Heal, Geoffrey, 1983. "Necessary and sufficient conditions for a resolution of the social choice paradox," Journal of Economic Theory, Elsevier, vol. 31(1), pages 68-87, October.
    12. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    13. Michael Miller & Daniel Osherson, 2009. "Methods for distance-based judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(4), pages 575-601, May.
    Full references (including those not matched with items on IDEAS)

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    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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