MATH 3094: Mathematics & Politics: Voting, Fair Division, and Conflict

Prerequisites: MATH 2710 and instructor consent.

This course applies mathematics to shed light on problems in the realm of politics, both domestic and international. We begin with a study of voting systems, including both electoral and legislative processes. By formalizing notions of fairness, we will work towards theorems that will inform just how fair we expect elections to be. Our discussion of fair division will revolve around the problem of distributing seats in the U.S. House of Representatives among the fifty states. We will explore various apportionment paradoxes (e.g. how could an increase in the total number of seats lead to a reduction in the number of seats assigned to a particular state?) through history anddetermine whether these are avoidable in the future. The development of methods to measure the political power of voting blocs and coalitions will inform our analysis of the apportionment problem and lead us to investigate political conflict via game theory.