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Probabilistic opinion pooling

Author

Listed:
  • Franz Dietrich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Christian List

    (LSE - London School of Economics and Political Science)

Abstract

This review article introduces and evaluates various ways to aggregate probabilistic opinions of different individuals. For each of these three ways, an axiomatic characterization result is presented (a new one in the case of multiplicative pooling). The three ways satisfy different axioms and are justifiable under different conditions. Linear pooling may be justified on procedural grounds, but not on epistemic grounds. Geometric and multiplicative pooling may be justified on epistemic grounds, but which of the two is appropriate depends not just on the opinion profiles to be aggregated but also on the information on which they are based. Geometric pooling can be justified if all individuals' opinions are based on the same information, while multiplicative pooling can be justified if every individual's opinions are based solely on private information, except for some shared background information held by everyone.
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Suggested Citation

  • Franz Dietrich & Christian List, 2016. "Probabilistic opinion pooling," Post-Print halshs-00978032, HAL.
    • Handle: RePEc:hal:journl:halshs-00978032
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    Citations

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    Cited by:

    1. Franz Dietrich & Christian List, 2017. "Probabilistic opinion pooling generalized. Part two: the premise-based approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 787-814, April.
    2. Elena M. Parilina & Georges Zaccour, 2022. "Sustainable Cooperation in Dynamic Games on Event Trees with Players’ Asymmetric Beliefs," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 92-120, July.
    3. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    4. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Documents de travail du Centre d'Economie de la Sorbonne 17028, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01539444, HAL.
    6. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    7. 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.
    8. Fioravanti, Federico, 2025. "Fuzzy classification aggregation," Mathematical Social Sciences, Elsevier, vol. 135(C).
    9. Ding, Huihui & Pivato, Marcus, 2021. "Deliberation and epistemic democracy," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 138-167.
    10. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    11. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Post-Print halshs-01539444, HAL.
    12. Marta O. Soares & Mark J. Sculpher & Karl Claxton, 2020. "Health Opportunity Costs: Assessing the Implications of Uncertainty Using Elicitation Methods with Experts," Medical Decision Making, , vol. 40(4), pages 448-459, May.
    13. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    14. Jared A. Beekman & Ronald F. A. Woodaman & Dennis M. Buede, 2020. "A Review of Probabilistic Opinion Pooling Algorithms with Application to Insider Threat Detection," Decision Analysis, INFORMS, vol. 17(1), pages 39-55, March.
    15. Federica Ceron & Vassili Vergopoulos, 2019. "Aggregation of Bayesian preferences: unanimity vs monotonicity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(3), pages 419-451, March.
    16. Liu, Zixuan & Lawry, Jonathan & Crosscombe, Michael, 2025. "Imprecise belief fusion improves multi-agent social learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 664(C).
    17. Dietrich, Franz, 2016. "A Theory Of Bayesian Groups," MPRA Paper 75363, University Library of Munich, Germany.
    18. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    19. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.

    More about this item

    Keywords

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    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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