Mathematics 150 - Voting and Elections

The outcomes of many elections, whether to elect the next United States president or to rank college football teams, can displease many of the voters. How can perfectly fair elections produce results that nobody likes? We will analyze different voting systems, including majority rule, plurality rule, Borda count, ranked choice voting, and approval voting, and assess a voter’s power to influence the election under each system, for example, by calculating the Banzhaf power index. We will prove Arrow’s Impossibility Theorem and discuss its implications. After exploring the pitfalls of various voting systems through both theoretical analysis and case studies, we will try to answer some pressing questions: Which voting system best reflects the will of the voters? Which is least susceptible to manipulation? What properties should we seek in a voting system, and how can we best attain them?

Fall semester. Professor Call

How to handle overenrollment: Preference given to first and second year students. Math majors and non-majors are welcome.

Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: May include problem sets, in-class group work, in-class quizzes or exams, take-home exams, and final projects.