We construct a model of an exchange economy in which agents trade assets contingent on an observable signal, the probability of which depends on public opinion. The agents in our model are replaced occasionally, and each person updates beliefs in response to observed outcomes. We show that the distribution of the observed signal is described by a quasi-nonergodic process and that people continue to disagree with each other forever. These disagreements generate large wealth inequalities that arise from the multiplicative nature of wealth dynamics, which makes successful bold bets highly profitable.