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Categorical versus graded beliefs

Author

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  • Franz Dietrich

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold beliefs of both types simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List. The nature, relevance, and implications of the tension are explained and assessed.

Suggested Citation

  • Franz Dietrich, 2022. "Categorical versus graded beliefs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03615028, HAL.
    • Handle: RePEc:hal:cesptp:halshs-03615028
    DOI: 10.3389/fpsyg.2022.817940
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03615028
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    References listed on IDEAS

    as
    1. Franz Dietrich & Christian List, 2018. "From degrees of belief to binary beliefs: Lessons from judgment-aggregation theory," PSE-Ecole d'économie de Paris (Postprint) halshs-01744085, HAL.
    2. Franz Dietrich & Christian List, 2019. "The relation between degrees of belief and binary beliefs: A general impossibility theorem," Documents de travail du Centre d'Economie de la Sorbonne 19001, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Minkyung Wang, 2024. "Aggregating individual credences into collective binary beliefs: an impossibility result," Theory and Decision, Springer, vol. 97(1), pages 39-66, August.

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    1. Franz Dietrich & Christian List, 2019. "The relation between degrees of belief and binary beliefs: A general impossibility theorem," Documents de travail du Centre d'Economie de la Sorbonne 19001, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Franz Dietrich & Christian List, 2019. "The relation between degrees of belief and binary beliefs: A general impossibility theorem," Documents de travail du Centre d'Economie de la Sorbonne 19001, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Dietrich, Franz & List, Christian, 2014. "From degrees of belief to beliefs: Lessons from judgment-aggregation theory," MPRA Paper 58257, University Library of Munich, Germany.
    4. Minkyung Wang, 2024. "Aggregating individual credences into collective binary beliefs: an impossibility result," Theory and Decision, Springer, vol. 97(1), pages 39-66, August.

    More about this item

    Keywords

    logic vs. rational choice theory; yes/no belief vs. graded belief; subjective probability; belief binarization; lottery paradox; impossibility theorem; binary belief; credence;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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