Modeling the Change of Paradigm: Non-Bayesian Reactions 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 Coherence, 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.