Paradoxes of infinite aggregation

There are infinitely many ways the world might be, and there may well be infinitely many people in it. These facts raise moral paradoxes. We explore a conflict between two highly attractive principles: a Pareto principle that says that what is better for everyone is better overall, and a statewise dominance principle that says that what is sure to turn out better is better on balance. We refine and generalize this paradox, showing that the problem is faced by many theories of interpersonal aggregation besides utilitarianism, and by many decision theories besides expected value theory. Considering the range of consistent responses, we find all of them to be quite radical.