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Do Bayesians Learn Their Way Out of Ambiguity?

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  • Alexander Zimper

    (Department of Economics, University of Pretoria, Hatfield 0028, South Africa)

Abstract

In standard models of Bayesian learning, agents reduce their uncertainty about an event's true probability because their consistent estimator concentrates almost surely around this probability's true value as the number of observations becomes large. This paper takes the empirically observed violations of Savage's (Savage, L. J. 1954. The Foundations of Statistics . John Wiley & Sons, New York) sure thing principle seriously and asks whether Bayesian learners with ambiguity attitudes will reduce their ambiguity when sample information becomes large. To address this question, I develop closed-form models of Bayesian learning in which beliefs are described as Choquet estimators with respect to neoadditive capacities (Chateauneuf, A., J. Eichberger, S. Grant. 2007. Choice under uncertainty with the best and worst in mind: Neo-additive capacities. J. Econom. Theory 137 (1) 538--567). Under the optimistic, the pessimistic, and the full Bayesian update rules, a Bayesian learner's ambiguity will increase rather than decrease to the effect that these agents will express ambiguity attitudes regardless of whether they have access to large sample information or not. Although consistent Bayesian learning occurs under the Sarin and Wakker (Sarin, R., P. P. Wakker. 1998b. Revealed likelihood and Knightian uncertainty. J. Risk Uncertainty 16 (3) 223--250) update rule, this result comes with the descriptive drawback that it does not apply to agents who still express ambiguity attitudes after one round of updating.

Suggested Citation

  • Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
  • Handle: RePEc:inm:ordeca:v:8:y:2011:i:4:p:269-285
    DOI: 10.1287/deca.1110.0217
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    Cited by:

    1. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    2. Nicky Nicholls & Aylit Romm & Alexander Zimper, 2015. "The impact of statistical learning on violations of the sure-thing principle," Journal of Risk and Uncertainty, Springer, vol. 50(2), pages 97-115, April.
    3. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    4. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.
    5. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Philippe Delquié & Kenneth C. Lichtendahl & Jason R. W. Merrick & Ahti Salo & George Wu, 2011. "From the Editors ---Probability Scoring Rules, Ambiguity, Multiattribute Terrorist Utility, and Sensitivity Analysis," Decision Analysis, INFORMS, vol. 8(4), pages 251-255, December.
    6. Alexander Zimper & Wei Ma, 2017. "Bayesian learning with multiple priors and nonvanishing ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 409-447, October.
    7. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors ---Group Decisions, Preference Elicitation, Experienced Utility, Survival Probabilities, and Portfolio Value of Information," Decision Analysis, INFORMS, vol. 10(2), pages 99-102, June.

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    More about this item

    Keywords

    nonadditive probability measures; Bayesian learning; Choquet expected utility theory;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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