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

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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.

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  • 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
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    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.
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    Cited by:

    1. Benoît, Jean-Pierre & Dubra, Juan, 2018. "When do populations polarize? An explanation," MPRA Paper 86173, University Library of Munich, Germany.
    2. Axel Anderson & Nikoloz Pkhakadze, 2023. "Polarizing Persuasion," Working Papers gueconwpa~23-23-04, Georgetown University, Department of Economics.
    3. Gabriel Martinez & Nicholas H. Tenev, 2020. "Optimal Echo Chambers," Papers 2010.01249, arXiv.org, revised Jun 2025.
    4. Anderson, Axel & Pkhakadze, Nikoloz, 2025. "Polarizing persuasion," Games and Economic Behavior, Elsevier, vol. 152(C), pages 181-198.
    5. Tuval Danenberg, 2025. "Bayesian Polarization," Papers 2509.02513, arXiv.org.
    6. Stone, Daniel, 2018. "Just a big misunderstanding? Bias and Bayesian affective polarization," SocArXiv 58sru, Center for Open Science.

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    Keywords

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    JEL classification:

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

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