Mathematics is of great use in many social sciences, as it is the sciences. There was a time when people argued that biology was too "complex" to use mathematics to get significant insights into the subject. I think people no longer think this. Unfortunately, many pieces of mathematics as they "stray" directly from mathematics itself into applications in other fields get "written off" by some people in the mathematics community. For example, Game Theory was pioneered by John Von Neumann and many mathematicians have made contributions to this beautiful subject. However, most of the research in game theory is now done by mathematically trained people (sometimes mathematicians) who teach in economics departments, political science departments, etc. rather than in mathematics departments.
There are many questions some of which arise in game theory but also in areas which have come to be called social choice theory, etc. which are very mathematical which deal with fairness questions of a variety of kinds. Examples include fair apportionment, fair division, fair games, bankruptcy, weighted votings, voting in general, etc. I have been trying to encourage mathematics departments to partner with interested parties to offer an interdisiplinary degree program which I call "fairness studies" which builds on what has been accomplished as of now and to train people to do more work in this area. So far, not a lot of interest.
Best,
Joe Malkevitch
