Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: We study belief revision when information is given as a set of relevant probability distributions. This flexible setting encompasses (i) the standard notion of information as an event (a subset of the state space), (ii) qualitative information (``A is more likely than B"), (iii) interval information (``chance of A is between ten and twenty percent"), and more. In this setting, we behaviorally characterize Inertial Updating: the decision maker (DM) selects a posterior belief from the provided information set that minimizes the subjective distance between her prior and the information. We introduce a notion of Bayesian updating for general information sets and characterize distances consistent with Bayesian updating, which we call Bayesian Divergence, via an axiom similar to the classic notion of Dynamic Consistency. Importantly, with general information, Bayesian updating is not unique, and two Bayesian DMs with a common prior may disagree after common information, resulting in polarization and speculative trade. We also behaviorally characterize Renyi and Kullback-Leibler divergences.

Written with Adam Dominiak and Matthew Kovach.