IDEAS home Printed from https://ideas.repec.org/p/wil/wileco/2016-18.html
   My bibliography  Save this paper

Dimensionality and Disagreement: Asymptotic Belief Divergence in Response to Common Information

Author

Listed:

Abstract

We provide a model of boundedly-rational, multidimensional learning and characterize when beliefs will converge to the truth. Agents maintain beliefs as marginal probabilities rather than joint probabilities, and agents' information is of lower dimension than the model. As a result, for some observations agents may face an identification problem affecting the role of data in inference. Beliefs converge to the truth when these observations are rare, but beliefs diverge when observations presenting an identification problem are frequent. Robustly, two agents with differing priors who observe identical, unambiguous information may disagree forever, with stronger disagreement the more information received.

Suggested Citation

  • Isaac Loh & Gregory Phelan, 2016. "Dimensionality and Disagreement: Asymptotic Belief Divergence in Response to Common Information," Department of Economics Working Papers 2016-18, Department of Economics, Williams College, revised Jan 2019.
    • Handle: RePEc:wil:wileco:2016-18
    as

    Download full text from publisher

    File URL: https://web.williams.edu/Economics/wp/LohPhelanDimensionalityDisagreement_Jan2019.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    2. Xavier Gabaix, 2014. "A Sparsity-Based Model of Bounded Rationality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(4), pages 1661-1710.
    3. Ignacio Esponda & Demian Pouzo, 2016. "Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models," Econometrica, Econometric Society, vol. 84, pages 1093-1130, May.
    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. Jean-Pierre Benoît & Juan Dubra, 2018. "When do populations polarize? An explanation," Documentos de Trabajo/Working Papers 1801, Facultad de Ciencias Empresariales y Economia. Universidad de Montevideo..
    2. Stone, Daniel, 2018. "Just a big misunderstanding? Bias and Bayesian affective polarization," SocArXiv 58sru, Center for Open Science.
    3. Axel Anderson & Nikoloz Pkhakadze, 2023. "Polarizing Persuasion," Working Papers gueconwpa~23-23-04, Georgetown University, Department of Economics.
    4. Gabriel Martinez & Nicholas H. Tenev, 2020. "Optimal Echo Chambers," Papers 2010.01249, arXiv.org, revised Feb 2024.

    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. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    2. Kubler, Felix & Scheidegger, Simon, 2023. "Uniformly self-justified equilibria," Journal of Economic Theory, Elsevier, vol. 212(C).
    3. Vedolin, Andrea & Molavi, Pooya & Tahbaz-Salehi, Alireza, 2021. "Model Complexity, Expectations, and Asset Prices," CEPR Discussion Papers 15717, C.E.P.R. Discussion Papers.
    4. Geoffroy de Clippel & Kareen Rozen, 2020. "Relaxed Optimization: e-Rationalizability and the FOC-Departure Index in Consumer Theory," Working Papers 2020-07, Brown University, Department of Economics.
    5. Ignacio Esponda & Emanuel Vespa & Sevgi Yuksel, 2024. "Mental Models and Learning: The Case of Base-Rate Neglect," American Economic Review, American Economic Association, vol. 114(3), pages 752-782, March.
    6. Geoffroy de Clippel & Kareen Rozen, 2018. "Consumer Theory with Misperceived Tastes," Working Papers 2018-10, Brown University, Department of Economics.
    7. Little, Andrew T., 2022. "Information Theory and Biased Beliefs," OSF Preprints vfqy2_v1, Center for Open Science.
    8. Olivier Compte, 2023. "Belief formation and the persistence of biased beliefs," Papers 2310.08466, arXiv.org.
    9. Ignacio Esponda & Demian Pouzo, 2017. "Conditional Retrospective Voting in Large Elections," American Economic Journal: Microeconomics, American Economic Association, vol. 9(2), pages 54-75, May.
    10. Joshua Schwartzstein & Adi Sunderam, 2021. "Using Models to Persuade," American Economic Review, American Economic Association, vol. 111(1), pages 276-323, January.
    11. Schipper, Burkhard C., 2021. "Discovery and equilibrium in games with unawareness," Journal of Economic Theory, Elsevier, vol. 198(C).
    12. V. Bhaskar & Caroline Thomas, 2019. "The Culture of Overconfidence," American Economic Review: Insights, American Economic Association, vol. 1(1), pages 95-110, June.
    13. Gamp, Tobias & Krähmer, Daniel, 2022. "Biased Beliefs in Search Markets," Rationality and Competition Discussion Paper Series 365, CRC TRR 190 Rationality and Competition.
    14. Yingkai Li & Aleksandrs Slivkins, 2022. "Exploration and Incentivizing Participation in Randomized Trials," Papers 2202.06191, arXiv.org, revised Mar 2025.
    15. Marek Weretka & Daniel Quint, 2022. "Slope-takers in anonymous markets," GRAPE Working Papers 64, GRAPE Group for Research in Applied Economics.
    16. Bohren, Aislinn & Hauser, Daniel, 2017. "Learning with Heterogeneous Misspecified Models: Characterization and Robustness," CEPR Discussion Papers 12036, C.E.P.R. Discussion Papers.
    17. Hagenbach, Jeanne & Koessler, Frédéric, 2017. "The Streisand effect: Signaling and partial sophistication," Journal of Economic Behavior & Organization, Elsevier, vol. 143(C), pages 1-8.
    18. Philippe Jehiel & Konrad Mierendorff, 2021. "Auction Design with Data-Driven Misspecifications," Papers 2107.00640, arXiv.org.
    19. Jeanne Hagenbach & Frédéric Koessler, 2019. "Partial Language Competence," Working Papers hal-03393108, HAL.
    20. Glazer, Jacob & Rubinstein, Ariel, 2024. "Making predictions based on data: Holistic and atomistic procedures," Journal of Economic Theory, Elsevier, vol. 216(C).

    More about this item

    Keywords

    Heterogeneous beliefs; divergence; learning; Bayesian updating; bounded rationality; sparsity;
    All these keywords.

    JEL classification:

    • D10 - Microeconomics - - Household Behavior - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

    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:wil:wileco:2016-18. 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: Greg Phelan (email available below). General contact details of provider: https://edirc.repec.org/data/edwilus.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.