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Propositionwise judgment aggregation: the general case

Author

Listed:
  • Franz Dietrich

    (CERSES - UMR 8137 - Centre de recherche sens, ethique, société - UPD5 - Université Paris Descartes - Paris 5 - CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Christian List

    (LSE - London School of Economics and Political Science)

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 (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a).

Suggested Citation

  • Franz Dietrich & Christian List, 2013. "Propositionwise judgment aggregation: the general case," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00978004, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00978004
    DOI: 10.1007/s00355-012-0661-7
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    References listed on IDEAS

    as
    1. 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.
    2. Mongin, Philippe, 2008. "Factoring out the impossibility of logical aggregation," Journal of Economic Theory, Elsevier, vol. 141(1), pages 100-113, July.
    3. Anand, Paul & Pattanaik, Prasanta & Puppe, Clemens (ed.), 2009. "The Handbook of Rational and Social Choice," OUP Catalogue, Oxford University Press, number 9780199290420.
    4. List, Christian, 2003. "A possibility theorem on aggregation over multiple interconnected propositions," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 1-13, February.
    5. Dietrich, Franz & Mongin, Philippe, 2010. "The premiss-based approach to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 562-582, March.
    6. List, Christian, 2004. "A Model of Path-Dependence in Decisions over Multiple Propositions," American Political Science Review, Cambridge University Press, vol. 98(3), pages 495-513, August.
    7. 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.
    8. Duggan, John, 1999. "A General Extension Theorem for Binary Relations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 1-16, May.
    9. 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.
    10. List, Christian & Pettit, Philip, 2002. "Aggregating Sets of Judgments: An Impossibility Result," Economics and Philosophy, Cambridge University Press, vol. 18(1), pages 89-110, April.
    11. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    12. Nehring, Klaus, 2003. "Arrow's theorem as a corollary," Economics Letters, Elsevier, vol. 80(3), pages 379-382, September.
    13. 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.
    14. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ruth Ben-Yashar & Shmuel Nitzan, 2017. "Are two better than one? A note," Public Choice, Springer, vol. 171(3), pages 323-329, June.
    2. 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, vol. 48(4), pages 747-786, April.
    3. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    4. Ben-Yashar, Ruth & Nitzan, Shmuel, 2019. "Skill, value and remuneration in committees," Economics Letters, Elsevier, vol. 174(C), pages 93-95.
    5. Ben-Yashar, Ruth & Danziger, Leif, 2016. "The unanimity rule and extremely asymmetric committees," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 107-112.
    6. 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.
    7. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    8. Luigi Marengo & Simona Settepanella & Yan X. Zhang, 2021. "Towards a unified aggregation framework for preferences and judgments," Evolutionary and Institutional Economics Review, Springer, vol. 18(1), pages 21-44, April.
    9. Ruth Ben-Yashar & Miriam Krausz & Shmuel Nitzan, 2018. "Government loan guarantees and the credit decision-making structure," Canadian Journal of Economics, Canadian Economics Association, vol. 51(2), pages 607-625, May.
    10. repec:hal:pseose:halshs-01249513 is not listed on IDEAS
    11. Ruth Ben-Yashar & Miriam Krausz & Shmuel Nitzan, 2018. "The effect of democratic decision-making on investment in reputation," Public Choice, Springer, vol. 177(1), pages 155-164, October.
    12. BAHARAD, Eyal & BEN-YASHAR, Ruth & NITZAN, Shmuel, 2018. "Variable Competence and Collective Performance: Unanimity vs. Simple Majority Rule," Discussion paper series HIAS-E-80, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    13. Ruth Ben-Yashar & Shmuel Nitzan, 2017. "Is diversity in capabilities desirable when adding decision makers?," Theory and Decision, Springer, vol. 82(3), pages 395-402, March.
    14. Eyal Baharad & Ruth Ben-Yashar, 2021. "Judgment Aggregation by a Boundedly Rational Decision-Maker," Group Decision and Negotiation, Springer, vol. 30(4), pages 903-914, August.
    15. Shmuel Nitzan & Tomoya Tajika, 2022. "Inequality of decision-makers’ power and marginal contribution," Theory and Decision, Springer, vol. 92(2), pages 275-292, March.
    16. Ruth Ben-Yashar, 2023. "An application of simple majority rule to a group with an even number of voters," Theory and Decision, Springer, vol. 94(1), pages 83-95, January.
    17. Ruth Ben-Yashar & Shmuel Nitzan & Tomoya Tajika, 2021. "Skill, power and marginal contribution in committees," Journal of Theoretical Politics, , vol. 33(2), pages 225-235, April.
    18. Dietrich, Franz & List, Christian, 2014. "From degrees of belief to beliefs: Lessons from judgment-aggregation theory," MPRA Paper 58257, University Library of Munich, Germany.
    19. Eyal Baharad & Ruth Ben-Yashar & Shmuel Nitzan, 2020. "Variable Competence and Collective Performance: Unanimity Versus Simple Majority Rule," Group Decision and Negotiation, Springer, vol. 29(1), pages 157-167, February.

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    More about this item

    Keywords

    judgment aggregation; impossibility theorems; independence axiom; taxonomy;
    All these keywords.

    JEL classification:

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

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