We consider collective decisions under uncertainty, when agents have generalized Hurwicz preferences, a broad class allowing many different ambiguity attitudes, including subjective expected utility preferences. We consider sequences of acts that are ``almost-objectively uncertain'' in the sense that asymptotically, all agents almost agree about the probabilities of the underlying events. We introduce a Pareto axiom, which applies only to asymptotic preferences along such almost-objective sequences. This axiom implies that the social welfare function is utilitarian, but it does not impose any constraint on collective beliefs. Next, we show that a Pareto axiom restricted to two-valued acts implies that collective beliefs are contained in the closed, convex hull of individual beliefs, but imposes no constraints on the social welfare function. Neither axiom entails any link between individual and collective ambiguity attitudes.