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.
