Updating Beliefs with Ambiguous Evidence: Implications for Polarization

Abstract

We introduce and analyze a model in which agents observe sequences of signals about the state of the world, some of which are ambiguous and open to interpretation. Instead of using Bayes' rule on the whole sequence, our decision makers use Bayes' rule in an iterative way: first to interpret each signal and then to form a posterior on the whole sequence of interpreted signals. This technique is computationally efficient, but loses some information since only the interpretation of the signals is retained and not the full signal. We show that such rules are optimal if agents sufficiently discount the future; while if they are very patient then a time-varying random interpretation rule becomes optimal. One of our main contributions is showing that the model provides a formal foundation for why agents who observe exactly the same stream of information can end up becoming increasingly polarized in their posteriors.