Lectures: Tuesdays and Thursdays 1:00-2:15 via Zoom.

Instructor: Gregg Musiker (musiker "at" math.umn.edu)

Office Hours: Tuesdays 3:30-4:30, Thursdays 11:00-12:00, Fridays 10:00 - 11:00 via Zoom; also by appointment.

Course Description:

Choices come up in life all the time: selecting a restaurant option among a group of people, choosing the best picture nominees for that year?s Oscars, ranking NCAA sports teams, holding an election for political office, matching jobs to candidates, or in many other social situations. The course will explore different voting systems, including single vote plurality, instant run-off (also known as ranked choice), Borda count systems, approval voting, and the mathematics behind them. While Arrow?s theorem states that no electoral system can be completely fair, we will study the strengths and weaknesses of each system, both in mathematical theory as well as historical events. Mathematical measurements of power, such as Banzhaf index and Shapley-Shubik, apportionment methods and paradoxes, fair division, basic game theory and matching algorithms may also be covered. We will also discuss Gerrymandering, both from geometric and probabilistic points of view and how this relates to recent Supreme Court cases.

Required text: Mathematics and Politics: Stategy, Voting, Power, and Proof, by Alan D. Taylor and Allison M. Pacelli.