This paper studies social choice correspondences assigning a set of choices to each pair consisting of a nonempty subset of the set of alternatives and a weak preference profile, which is called an extended social choice correspondence (ESCC). The ESCC satisfies unanimity if, when there is a weakly Pareto dominant alternative, the ESCC selects this alternative. Stability requires that the ESCC is immune to manipulation through withdrawal of some alternatives. Independence implies that the ESCC 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 ESCC satisfying the three axioms, when the set of alternatives is finite but includes more than three alternatives, and the set of voters can have any cardinality. Our main theorem establishes that the ESCC satisfying the three axioms is a serial dictatorship ala Eraslan and McLennan (2004). Our second theorem shows that a serial dictatorship includes ‘invisible serial dictators’ ala Kirman and Sondermann (1972).
