Do Bayesians learn their way out of ambiguity?

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 (1954) 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 neo-additive capacities (Chateauneuf, Eichberger, and Grant 2007). Under the optimistic, the pessimistic, and the full Bayesian update rule, a Bayesian learner s ambiguity will increase rather than decrease to the e¤ect that these agents will express ambiguity attitudes regardless of whether they have access to large sample information or not. While consistent Bayesian learning occurs under the Sarin-Wakker 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.