The implementability of liberalism
本文证明在无限制偏好域下，存在既满足选择自由主义又可通过纳什均衡实施的社会选择规则，当且仅当至少有三个参与者且结果集大小至少是参与者数的两倍。
Abstract This note shows that under the unrestricted domain, there exists a choice 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 choice liberal if and only if for every player, there exists at least one pair of outcomes such that if this player strictly prefers one over the other, the one he prefers is socially desirable and the other one is not. A social choice rule is Nash implementable if and only if there exists a mechanism such that at every preference profile, the set of Nash equilibrium outcomes coincides with the set of socially desirable ones. The proof constructs an intuitive Nash implementing mechanism.