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From degrees of belief to beliefs: Lessons from judgment-aggregation theory

Author

Listed:
  • Dietrich, Franz
  • List, Christian

Abstract

What is the relationship between degrees of belief and (all-or-nothing) beliefs? Can the latter be expressed as a function of the former, without running into paradoxes? We reassess this “belief-binarization” problem from the perspective of judgmentaggregation theory. Although some similarities between belief binarization and judgment aggregation have been noted before, the literature contains no general study of the implications of aggregation-theoretic impossibility and possibility results for belief binarization. We seek to fill this gap. At the centre of this paper is an impossibility theorem showing that, except in simple cases, there exists no belief-binarization rule satisfying four baseline desiderata (“universal domain”, “belief consistency and completeness”, “propositionwise independence”, “certainty preservation”). We show that this result is a corollary of the judgment-aggregation variant of Arrow’s impossibility theorem and explore several escape routes from it.

Suggested Citation

  • Dietrich, Franz & List, Christian, 2014. "From degrees of belief to beliefs: Lessons from judgment-aggregation theory," MPRA Paper 58257, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:58257
    as

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    File URL: https://mpra.ub.uni-muenchen.de/80844/1/MPRA_paper_80844.pdf
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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. Kornhauser, Lewis A., 1992. "Modeling collegial courts I: Path-dependence," International Review of Law and Economics, Elsevier, vol. 12(2), pages 169-185, June.
    3. 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.
    4. 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.
    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. Douven, Igor & Romeijn, Jan-Willem, 2007. "The Discursive Dilemma As A Lottery Paradox," Economics and Philosophy, Cambridge University Press, vol. 23(3), pages 301-319, November.
    7. Kornhauser, Lewis A, 1992. "Modeling Collegial Courts. II. Legal Doctrine," Journal of Law, Economics, and Organization, Oxford University Press, vol. 8(3), pages 441-470, October.
    8. Dietrich, Franz, 2006. "Judgment aggregation: (im)possibility theorems," Journal of Economic Theory, Elsevier, vol. 126(1), pages 286-298, January.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    subjective probability; yes/no belif; impossibility theorem on binarization; analytic philosophy; judgment aggregation;

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D0 - Microeconomics - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D89 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Other

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