Bayesian Social Aggregation with Accumulating Evidence

How should we aggregate the ex ante preferences of Bayesian agents with heterogeneous beliefs? Suppose the state of the world is described by a random process that unfolds over time. Different agents have different beliefs about the probabilistic laws governing this process. As new information is revealed over time by the process, agents update their beliefs and preferences via Bayes rule. Consider a Pareto principle that applies only to preferences which remain stable in the long run under these updates. I show that this “asymptotic” Pareto principle implies that the social planner must be a utilitarian. But it does not impose any relationship between the beliefs of the individuals and those of the planner