Can someone tell me which mathematicians are actively working on social choice theory, or point to a place where they may be listed?

A. Slinko publishes in social choice theory. (I am presently unable to post this answer as a comment to the OP's question.) 


The Center for the Study of Rationality at the Hebrew University of Jerusalem studies social choice theory among other things. See their members list for a list of quite a few mathematicians who have worked on social choice theory. 


Graciela Chichilnisky is one of them (as well as her coauthors). Late Beno Eckmann has a nice chapter in one of his books on social choice theory as a direct application of an average rule in arbitrary spaces. Other people include Luc Lauwers or Shmuel Weinberger. These are examples of mainly algebraic topology at work. On the other hand, social choice theory is a wide area. It ranges from aggregating preferences to voting and even mechanism design to some extent where tools applied are different. 

