THE IMPLEMENTABILITY OF SEN’S LIBERALISM

ABSTRACT: This note shows that under the unrestricted preference domain, there exists a liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A social choice rule is liberal if and only if for every player, there exists a pair of outcomes such that if this player strictly prefers one over the other, the one she prefers is socially optimal and the other one is not. A social choice rule is Nash implementable if and only if there exists a mechanism whose set of Nash equilibrium outcomes coincides with the set of socially optimal ones for every preference profile. The proof constructs an intuitive Nash implementing mechanism.

KEYWORDS: liberalism, Nash equilibrium, mechanism, implementation.

JEL CODES: D71, D82

WORD COUNT: 1,636

STATUS: In progress.

DRAFT: Available here.