Explorations on monotonicity in social choice theory

Due to Maskin (1977), Maskin-monotonicity is known to be a necessary condition for Nash-implementability. Once one classifies social choice rules as the ones which are Maskin-monotonic and those which are not, a natural question one may ask is whether it is possible to further classify the Maskinmonotonic social choice rules according to how strongly monotonic they are. This study utilizes two key notions , namely self-monotonicity and center, which enable us to compare Maskin-monotonic social choice rules among themselves according to the strength of their monotonicities. Moreover, Nashimplementable two-person social choice rules are now characterized via the notion of center, in line with the conjecture that Implementation Theory can be rewritten in terms of monotonicity