IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/29573.html
   My bibliography  Save this paper

Bayesian group belief

Author

Listed:
  • Dietrich, Franz

Abstract

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of the group members. The group members may have different information, different prior beliefs and even different domains (algebras) within which they hold beliefs, accounting for differences in awareness and conceptualisation. As is shown, group beliefs can incorporate all information spread across individuals without individuals having to explicitly communicate their information (that may be too complex or personal to describe, or not describable in principle in the language). The group beliefs derived here take a simple multiplicative form if people's information is independent (and a more complex form if information overlaps arbitrarily). This form contrasts with familiar linear or geometric opinion pooling and the (Pareto) requirement of respecting unanimous beliefs.

Suggested Citation

  • Dietrich, Franz, 2010. "Bayesian group belief," LSE Research Online Documents on Economics 29573, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:29573
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/29573/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dietrich, F.K. & List, C., 2007. "Opinion pooling on general agendas"," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    3. Mark J. Schervish & Teddy Seidenfeld & Joseph B. Kadane, 1991. "Shared Preferences and State-Dependent Utilities," Management Science, INFORMS, vol. 37(12), pages 1575-1589, December.
    4. Franz Dietrich, 2004. "Opinion Pooling under Asymmetric Information," Public Economics 0407002, University Library of Munich, Germany.
    5. Peter A. Morris, 1974. "Decision Analysis Expert Use," Management Science, INFORMS, vol. 20(9), pages 1233-1241, May.
    6. Pivato, Marcus, 2008. "The Discursive Dilemma and Probabilistic Judgement Aggregation," MPRA Paper 8412, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. List, Christian, 2010. "The theory of judgment aggregation: an introductory review," LSE Research Online Documents on Economics 27596, London School of Economics and Political Science, LSE Library.
    4. 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.
    5. Dietrich, Franz, 2016. "A Theory Of Bayesian Groups," MPRA Paper 75363, University Library of Munich, Germany.
    6. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    7. Franz Dietrich & Christian List, 2021. "Dynamically rational judgment aggregation," Post-Print halshs-03140090, HAL.
    8. Ruth Ben-Yashar & Leif Danziger, 2015. "When is voting optimal?," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 341-356, October.
    9. 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.
    10. Francesco Billari & Rebecca Graziani & Eugenio Melilli, 2014. "Stochastic Population Forecasting Based on Combinations of Expert Evaluations Within the Bayesian Paradigm," Demography, Springer;Population Association of America (PAA), vol. 51(5), pages 1933-1954, October.
    11. Philip E. Tetlock & Christopher Karvetski & Ville A. Satopää & Kevin Chen, 2024. "Long‐range subjective‐probability forecasts of slow‐motion variables in world politics: Exploring limits on expert judgment," Futures & Foresight Science, John Wiley & Sons, vol. 6(1), March.
    12. Satopää, Ville A. & Salikhov, Marat & Tetlock, Philip E. & Mellers, Barbara, 2023. "Decomposing the effects of crowd-wisdom aggregators: The bias–information–noise (BIN) model," International Journal of Forecasting, Elsevier, vol. 39(1), pages 470-485.
    13. Dietrich, F.K. & List, C., 2008. "The aggregation of propositional attitudes: towards a general theory," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Dietrich, Franz & List, Christian & Bradley, Richard, 2012. "A Joint Characterization of Belief Revision Rules," MPRA Paper 41240, University Library of Munich, Germany.
    15. Aurélien Baillon & Laure Cabantous & Peter Wakker, 2012. "Aggregating imprecise or conflicting beliefs: An experimental investigation using modern ambiguity theories," Journal of Risk and Uncertainty, Springer, vol. 44(2), pages 115-147, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. List, Christian, 2010. "The theory of judgment aggregation: an introductory review," LSE Research Online Documents on Economics 27596, London School of Economics and Political Science, LSE Library.
    2. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 427-452, July.
    3. Dietrich, F.K. & List, C., 2008. "The aggregation of propositional attitudes: towards a general theory," Research Memorandum 047, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. 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.
    5. Mongin, Philippe, 1998. "The paradox of the Bayesian experts and state-dependent utility theory," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 331-361, April.
    6. Pivato, Marcus, 2022. "Bayesian social aggregation with accumulating evidence," Journal of Economic Theory, Elsevier, vol. 200(C).
    7. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    8. Itai Sher, 2020. "How perspective-based aggregation undermines the Pareto principle," Politics, Philosophy & Economics, , vol. 19(2), pages 182-205, May.
    9. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    10. Edi Karni & Philippe Mongin, 2000. "On the Determination of Subjective Probability by Choices," Management Science, INFORMS, vol. 46(2), pages 233-248, February.
    11. Eric Danan & Thibault Gajdos & Jean-Marc Tallon, 2015. "Harsanyi's Aggregation Theorem with Incomplete Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 7(1), pages 61-69, February.
    12. List, Christian & Polak, Ben, 2010. "Introduction to judgment aggregation," Journal of Economic Theory, Elsevier, vol. 145(2), pages 441-466, March.
    13. Crès, Hervé & Tvede, Mich, 2022. "Aggregation of opinions in networks of individuals and collectives," Journal of Economic Theory, Elsevier, vol. 199(C).
    14. Ellina, Polina & Mascarenhas, Briance & Theodossiou, Panayiotis, 2020. "Clarifying managerial biases using a probabilistic framework," Journal of Behavioral and Experimental Finance, Elsevier, vol. 27(C).
    15. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    16. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    17. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    18. Ed Cook & Jason R. W. Merrick, 2023. "Technology Implementation at Capital One," Interfaces, INFORMS, vol. 53(3), pages 178-191, May.
    19. Christian Gollier, 2007. "Whom should we believe? Aggregation of heterogeneous beliefs," Journal of Risk and Uncertainty, Springer, vol. 35(2), pages 107-127, October.
    20. Kolm, Serge-Christophe, 1998. "Chance and justice: Social policies and the Harsanyi-Vickrey-Rawls problem," European Economic Review, Elsevier, vol. 42(8), pages 1393-1416, September.

    More about this item

    Keywords

    utility-theory; aggregation; opinion pooling; Bayesianism; axiomatic approach; subjective probability; ISI;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:29573. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.