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Propositionwise judgment aggregation: the general case

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  • Franz Dietrich

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  • Christian List

Abstract

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or extended unanimity preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between, 2002 ), Nehring (Oligarchies in judgment aggregation: a characterization, 2006 ), Dietrich and List (Soc Choice Welf 29(1):19–33, 2007a ) and Dokow and Holzman (J Econ Theory 145(2):495–511, 2010a ). Copyright The Author(s) 2013

Suggested Citation

  • Franz Dietrich & Christian List, 2013. "Propositionwise judgment aggregation: the general case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1067-1095, April.
  • Handle: RePEc:spr:sochwe:v:40:y:2013:i:4:p:1067-1095 DOI: 10.1007/s00355-012-0661-7
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    References listed on IDEAS

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    1. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    2. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(01), pages 89-110, April.
    3. Marcus Pivato, 2009. "Geometric models of consistent judgement aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(4), pages 559-574, November.
    4. Franz Dietrich, 2007. "A generalised model of judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 529-565, June.
    5. Franz Dietrich & Christian List, 2008. "Judgment aggregation without full rationality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 15-39, June.
    6. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    7. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
    8. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    9. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    10. Klaus Nehring & Clemens Puppe, 2008. "Consistent judgement aggregation: the truth-functional case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 41-57, June.
    11. 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.
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    Cited by:

    1. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part one: general agendas," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, pages 747-786.
    2. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    3. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, pages 113-136.
    4. Ruth Ben-Yashar & Leif Danziger, 2014. "On the optimal composition of committees," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 973-980, December.
    5. repec:kap:theord:v:82:y:2017:i:3:d:10.1007_s11238-016-9570-z is not listed on IDEAS
    6. BEN-YASHAR, Ruth & NITZAN, Shmuel, 2016. "Is Diversity in Capabilities Desirable When Adding Decision Makers?," Discussion paper series HIAS-E-21, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    7. Ben-Yashar, Ruth & Danziger, Leif, 2016. "The unanimity rule and extremely asymmetric committees," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 107-112.
    8. BEN-YASHAR, Ruth & KRAUSZ, Miriam & NITZAN, Shmuel, 2017. "The Effect of Democratic Decision Making on Investment in Reputation," Discussion paper series HIAS-E-59, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    9. Dietrich, Franz & List, Christian, 2014. "From degrees of belief to beliefs: Lessons from judgment-aggregation theory," MPRA Paper 58257, University Library of Munich, Germany.
    10. repec:kap:pubcho:v:171:y:2017:i:3:d:10.1007_s11127-017-0439-7 is not listed on IDEAS
    11. repec:hal:journl:halshs-01249513 is not listed on IDEAS
    12. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.

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    JEL classification:

    • J50 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - General

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