Find out about Arrow's Theorem. How are voting methods evaluated?
Investigate a couple of different voting methods. In what ways do they
fail to be ideal? What kind of paradoxes arise?
Voting Theory
The following three books will be on reserve in library. They each have a
chapter on Voting Theory.
Excursions in Modern Mathematics by Tannenbaum and Arnold
For All Practical Purposes by COMAP
Mathematics Beyond the Numbers by Gilbert and Hatcher
The library also has "Basic geometry of voting" by Donald Saari
(JF1001.S225 1995). The math in this book is more advanced than that
found in the previous three books, but it might give you a sense of
the kind of mathematics that can be applied to analyzing voting.