Pseudo‐Bayesian updating

Abstract

I propose an axiomatic framework for belief revision when new information is qualitative, of the form “event A is at least as likely as event B .” My decision maker need not have beliefs about the joint distribution of the signal she will receive and the payoff‐relevant states. I propose three axioms, Exchangeability , Stationarity , and Reduction , to characterize the class of pseudo‐Bayesian updating rules. The key axiom, Exchangeability , requires that the order in which the information arrives does not matter if the different pieces of information neither reinforce nor contradict each other. I show that adding one more axiom, Conservatism , which requires that the decision maker adjust her beliefs just enough to embrace new information, yields Kullback–Leibler minimization: The decision maker selects the posterior closest to her prior in terms of Kullback–Leibler divergence from the probability measures consistent with newly received information. I show that pseudo‐Bayesian agents are susceptible to recency bias, which may be mitigated by repetitive learning.