203 - Social choice theory

Summary

Social choice theory is a formal analysis of collective decision-making rules, which construct a consistent social ranking of a set of alternatives on the basis of individual preferences over this set. Modern social choice theory begins with Kenneth J. Arrow’s impossibility theorem. According to Arrow’s theorem, there exists no collective decision-making rule that simultaneously satisfies four seemingly uncontroversial conditions; (1) unrestricted domain (a collective decision-making rule can take all logically possible orderings as its domain); (2) Pareto (if all individuals strictly prefer alternative x to y, then society would rank x above y); (3) independence of irrelevant alternatives (the social ranking of two alternatives depends only on individuals’ preferences over these two alternatives); and (4) nondictatorship (the social ranking does not coincide with the ranking of an identified individual, whatever others may rank). This theorem is understood as a generalization of Condorcet’s voting paradox (the majority rule may yield cyclical ranking of three alternatives). Arrow’s theorem provoked the large body of work on axiomatic analysis of distributive principles, including Rawls’s difference principle.