Bayesian social aggregation with accumulating evidence

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