In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique upper-continuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a...

In this paper I consider social choices under uncertainty. I prove that any social choice rule that satisfies independence of irrelevant alternatives, translation invariance, and weak anonymity is consistent with ex post Bayesian utilitarianism.