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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," Post-Print halshs-00978004, HAL.
    • Handle: RePEc:hal:journl:halshs-00978004
    DOI: 10.1007/s00355-012-0661-7
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    Cited by:

    1. Dietrich, Franz, 2015. "Aggregation theory and the relevance of some issues to others," Journal of Economic Theory, Elsevier, vol. 160(C), pages 463-493.
    2. Ben-Yashar, Ruth & Nitzan, Shmuel, 2019. "Skill, value and remuneration in committees," Economics Letters, Elsevier, vol. 174(C), pages 93-95.
    3. 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.
    4. repec:hal:pseose:halshs-01249513 is not listed on IDEAS
    5. 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.
    6. Dietrich, Franz, 2016. "Judgment aggregation and agenda manipulation," Games and Economic Behavior, Elsevier, vol. 95(C), pages 113-136.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Ben-Yashar, Ruth & Danziger, Leif, 2016. "The unanimity rule and extremely asymmetric committees," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 107-112.
    12. 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.
    13. Dietrich, Franz & List, Christian, 2014. "From degrees of belief to beliefs: Lessons from judgment-aggregation theory," MPRA Paper 58257, University Library of Munich, Germany.
    14. 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.
    15. Ruth Ben-Yashar & Shmuel Nitzan, 2017. "Are two better than one? A note," Public Choice, Springer, vol. 171(3), pages 323-329, June.
    16. 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.
    17. Ruth Ben‐Yashar & Miriam Krausz & Shmuel Nitzan, 2023. "Sovereign debt assistance and democratic decision‐making," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(5), pages 930-943, October.
    18. 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.
    19. Shmuel Nitzan & Tomoya Tajika, 2022. "Inequality of decision-makers’ power and marginal contribution," Theory and Decision, Springer, vol. 92(2), pages 275-292, March.
    20. 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.

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    JEL classification:

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

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