On the impossibility of preference aggregation under uncertainty.

We provide a general theorem on the aggregation of preferences under uncertainty. We study, in the Anscombe-Aumann setting a wide class of preferences that includes most known models of decision under uncertainty (and state-dependent versions of these models). We prove that aggregation is possible and necessarily linear if (society's) preferences are smooth. The latter means that society cannot have a non-neutral attitude towards uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate maxmin expected utility maximizers, even when they all have the same set of priors. We show that dropping a weak notion of monotonicity on society's preferences allows one to restore the possibility of aggregation of non-smooth preferences.