Abstract
This chapter focuses on social choice functions and correspondences. The chapter formalizes the collective decision problem by a mapping that selects for any given profile of preferences, that is, the data of one preference for each individual agent, a subset of outcomes, called the choice set, and interpreted as the set of collectively desirable outcomes for that profile. This mapping is a social choice correspondence—it summarizes a particular ethic of collective decisions, a compromising rule applicable to every possible configuration of individual preferences. All familiar voting methods satisfy three basic properties—(1) efficiency—the outcome should be Pareto optimal, (2) anonymity—every agent's opinion should influence equally the final decision, and (3) neutrality—no outcome should be a priori favoured by the social choice correspondence. A collective decision problem arises when a given set of individual agents must collectively select one among a given set of outcomes, whereas the respective opinions of these agents might conflict.
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