Arrow ’ s Theorem , countably many agents , and more visible invisible dictators ∗

For infinite societies, Fishburn (1970), Kirman and Sondermann (1972), and Armstrong (1980) gave a nonconstructive proof of the existence of a social welfare function satisfying Arrow’s conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving a concrete example of such a function, and (ii) showing how to compute, from a description of a profile on a pair of alternatives, which alternative is socially preferred under the function. The introduction of a certain “oracle” resolves Mihara’s impossibility result (1997) about computability of social welfare functions. Journal of Economic Literature Classifications: D71, C69, C71.