Essays in social choice theory

In this thesis, we investigate several issues concerning the class of Maskin monotonic social choice rules. Firstly, given a set of profiles, we find out which Maskin monotonic social choice rules adopt this set as a center. Then we introduce an algorithmic approach to find the self-monotonicities of a Maskin monotonic social choice rule. Moreover, we characterize all binary set operations that preserve Maskin monotonicity. Then we pass to investigating social choice functions, and determine the the domains of impossibility and possibility around a center with respect to a modified Manhattan metric. Finally, we try to reach a necessary and sufficient condition for Nash-implementability of a social choice in terms of neutrality