IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2305.08729.html
   My bibliography  Save this paper

Group knowledge and individual introspection

Author

Listed:
  • Michele Crescenzi

Abstract

We study distributed knowledge, which is what privately informed agents come to know by communicating freely with one another and sharing everything they know. Agents are not necessarily fully rational and differ in the ability to form higher-order knowledge. We model the inference making process that leads to distributed knowledge, and we do that by introducing revision operators and revision types. Since reasoning abilities can be heterogeneous, inference making turns out to be order dependent. We show that there are two qualitatively different cases of how distributed knowledge is attained. In the first, distributed knowledge is determined by any group member who can replicate all the inferences that anyone else in the group makes. This result is in line with the extant literature. In the second case, no member can replicate all the inferences that are made within the group. As a result, distributed knowledge is determined by any two group members who can jointly replicate what anyone else infers. This case can be interpreted as a form of wisdom of crowd effect and shows that, contrary to what is generally believed, distributed knowledge cannot always be reduced to the reasoning abilities of a single group member.

Suggested Citation

  • Michele Crescenzi, 2023. "Group knowledge and individual introspection," Papers 2305.08729, arXiv.org, revised Sep 2024.
  • Handle: RePEc:arx:papers:2305.08729
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2305.08729
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Evan Sadler, 2021. "A Practical Guide to Updating Beliefs From Contradictory Evidence," Econometrica, Econometric Society, vol. 89(1), pages 415-436, January.
    2. Bernard Monjardet, 2007. "Some Order Dualities In Logic, Games And Choices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 1-12.
    3. Robert J. Aumann, 1999. "Interactive epistemology I: Knowledge," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 263-300.
    4. Geanakoplos John, 2021. "Game Theory Without Partitions, and Applications to Speculation and Consensus," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 361-394, June.
    5. van der Hoek, Wiebe & van Linder, Bernd & Meyer, John-Jules, 1999. "Group knowledge is not always distributed (neither is it always implicit)," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 215-240, September.
    6. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, October.
    7. Samet, Dov, 1990. "Ignoring ignorance and agreeing to disagree," Journal of Economic Theory, Elsevier, vol. 52(1), pages 190-207, October.
    8. Mueller-Frank, Manuel, 2014. "Does one Bayesian make a difference?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 423-452.
    9. Morris, Stephen, 1996. "The Logic of Belief and Belief Change: A Decision Theoretic Approach," Journal of Economic Theory, Elsevier, vol. 69(1), pages 1-23, April.
    10. Basu, Pathikrit, 2019. "Bayesian updating rules and AGM belief revision," Journal of Economic Theory, Elsevier, vol. 179(C), pages 455-475.
    Full references (including those not matched with items on IDEAS)

    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. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    2. Gossner, Olivier & Tsakas, Elias, 2007. "Testing Rationality on Primitive Knowledge," Working Papers in Economics 275, University of Gothenburg, Department of Economics.
    3. John Geanakoplos, 1993. "Common Knowledge," Cowles Foundation Discussion Papers 1062, Cowles Foundation for Research in Economics, Yale University.
    4. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    5. Billot, Antoine & Vergopoulos, Vassili, 2018. "Expected utility without parsimony," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 14-21.
    6. Guilhem Lecouteux, 2018. "Bayesian game theorists and non-Bayesian players," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 25(6), pages 1420-1454, November.
    7. Fukuda, Satoshi, 2019. "Epistemic foundations for set-algebraic representations of knowledge," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 73-82.
    8. Robin Hanson, 2003. "For Bayesian Wannabes, Are Disagreements Not About Information?," Theory and Decision, Springer, vol. 54(2), pages 105-123, March.
    9. Tarbush, Bassel, 2016. "Counterfactuals in “agreeing to disagree” type results," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 125-133.
    10. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
    11. Gossner, O. & Tsakas, E., 2010. "A reasoning approach to introspection and unawareness," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. Alexander Zimper, 2010. "Canonical interpretation of propositions as events," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(3), pages 327-339, September.
    13. Olivier Gossner & Elias Tsakas, 2012. "Reasoning-based introspection," Theory and Decision, Springer, vol. 73(4), pages 513-523, October.
    14. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    15. Park, Hyoeun & Tayawa, Jason Paulo, 2024. "Anchored belief updating from recommendations," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    16. Meier, Martin, 2005. "On the nonexistence of universal information structures," Journal of Economic Theory, Elsevier, vol. 122(1), pages 132-139, May.
    17. Feinberg, Yossi, 2000. "Characterizing Common Priors in the Form of Posteriors," Journal of Economic Theory, Elsevier, vol. 91(2), pages 127-179, April.
    18. Fukuda, Satoshi, 2021. "Unawareness without AU Introspection," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    19. Samet, Dov, 2022. "The impossibility of agreeing to disagree: An extension of the sure-thing principle," Games and Economic Behavior, Elsevier, vol. 132(C), pages 390-399.
    20. Tsakas, Elias & Voorneveld, Mark, 2007. "Efficient communication, common knowledge, and consensus," Working Papers in Economics 255, University of Gothenburg, Department of Economics.

    More about this item

    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:arx:papers:2305.08729. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.