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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 des Ponts ParisTech - 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00978032, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00978032
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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. Dietrich, Franz & Spiekermann, Kai, 2012. "Independent opinions? on the causal foundations of belief formation and jury theorems," MPRA Paper 40137, University Library of Munich, Germany, revised Oct 2010.
    3. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations with abstentions," Journal of Economic Theory, Elsevier, vol. 145(2), pages 544-561, March.
    4. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    5. Franz Dietrich, 2010. "Bayesian group belief," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 595-626, October.
    6. Franz Dietrich & Christian List, 2007. "Arrow’s theorem in judgment aggregation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 19-33, July.
    7. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, vol. 20(9), pages 1233-1241, May.
    8. 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.
    9. Christopher Chambers, 2007. "An ordinal characterization of the linear opinion pool," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 457-474, December.
    10. Weymark, John A., 1997. "Aggregating Ordinal Probabilities on Finite Sets," Journal of Economic Theory, Elsevier, vol. 75(2), pages 407-432, August.
    11. Duddy, Conal & Piggins, Ashley, 2013. "Many-valued judgment aggregation: Characterizing the possibility/impossibility boundary," Journal of Economic Theory, Elsevier, vol. 148(2), pages 793-805.
    12. Dokow, Elad & Holzman, Ron, 2010. "Aggregation of binary evaluations," Journal of Economic Theory, Elsevier, vol. 145(2), pages 495-511, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ding, Huihui & Pivato, Marcus, 2021. "Deliberation and epistemic democracy," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 138-167.
    2. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    3. 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.
    4. 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.
    5. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Post-Print halshs-01539444, HAL.
    6. 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.
    7. Dietrich, Franz, 2016. "A Theory Of Bayesian Groups," MPRA Paper 75363, University Library of Munich, Germany.
    8. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    9. 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.
    10. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    11. 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.
    12. 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.
    13. 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.
    14. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    15. David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
    16. 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.
    17. Federica Ceron & Vassili Vergopoulos, 2017. "Aggregation of Bayesian preferences: Unanimity vs Monotonicity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01539444, HAL.

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    More about this item

    Keywords

    multiplicative pooling; geometric pooling; linear pooling; Bayesianism; aggregation of subjective probabilities;
    All these keywords.

    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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