Arrow's theorem, countably many agents, and more visible invisible dictators (Q1961954)

In the classical proof of Arrow's impossibility theorem, the assumption that the set of individuals is finite plays a central role. Furthermore, it was shown that this assumption is not only crucial to make the proof simpler, but also that it is a necessary part of the theorem itself: for infinite societies, there exists a social welfare function satisfying other Arrow's conditions. Several authors gave nonconstructive proofs of this existence. In this paper, the author gives a concrete example of such a social welfare function and shows how to compute, given two alternatives, which alternative is socially preferred under this function.