Algorithms for Social Choice Functions

Abstract

This paper will justify simple majority rule as a computational device which may be used to implement any social choice function which satisfies some plausible admissibility criteria. We take our cue from one of the author's previous papers (1976). The argument below improves upon Campbell (1976)-and, we would like to claim, upon rival procedures for generating non-empty choice sets-in several respects. First, the social choice functions are structured, not by an appeal to rationality desiderata, which are especially difficult to evaluate in the context of social choice, but by recognizing the value of the time taken to locate a member of the choice set.1 Second, majority rule is not assumed as the base relation used to generate choice sets; it is derived and the normative conditions employed are rather mild, certainly when compared to May (1952). Third, we investigate the decisiveness of the admissible social choice functions. Fourth, we give an argument very similar to the one of Kalai et al. (1976) defending our social choice functions in terms of incentive compatibility. Section 1 lays out the basic definitions and notation. Sections 2 and 3 consider the normative and computational aspects of social choice. The results are stated and discussed in Section 4; the proofs are relegated to an appendix. Section 5 addresses the question of incentive compatibility and Section 6 summarizes the paper.