2012) “Modeling the Change of Paradigm: Non-Bayesian Reaction to Unexpected News

Despite its normative appeal and widespread use, Bayes ’ rule has two well-known limitations: first, it does not predict how agents should react to an information to which they assigned probability zero; second, a sizable empirical evidence documents how agents systematically deviate from its prescriptions by overreacting to information to which they assigned a positive but small probability. By replacing Dynamic Consistency with a novel axiom, Dynamic Co-herence, we characterize an alternative updating rule that is not subject to these limitations, but at the same time coincides with Bayes ’ rule for “normal ” events. In particular, we model an agent with a utility function over consequences, a prior over priors ρ, and a threshold. In the first period she chooses the prior that maximizes the prior over priors ρ- a ’ la maximum likelihood. As new information is revealed: if the chosen prior assigns to this information a probability above the threshold, she follows Bayes ’ rule and updates it. Otherwise, she goes back to her prior over priors ρ, updates it using Bayes ’ rule, and then chooses the new prior that maximizes the updated ρ. We also extend our analysis to the case of ambiguity aversion