Social choice correspondences with infinitely many agents: serial dictatorship

We study social choice correspondences (SCC) assigning a set of choices to each pair consisting of a nonempty subset of the set of alternatives and a weak preference profile. The SCC satisfies unanimity if when there is a weakly Pareto dominant alternative, the SCC selects this alternative. Stability requires that the SCC is unaffected by withdrawal of losing alternatives. Independence implies that the SCC selects the same outcome from a subset of the set of alternatives for two preference profiles that are the same on this set. We characterize the SCC satisfying the three axioms, when the set of alternatives is finite but includes more than three alternatives, and the set of agents can have any cardinality. We show that the SCC is a serial dictatorship à la Eraslan and McLennan (J Econ Theory 117:29–54, 2004) and that a serial dictatorship can include “invisible serial dictators” à la Kirman and Sondermann (J Econ Theory 5:267–277, 1972).