Tanya L. Leise (Section 01)
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, 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 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?
Limited to 24 students. Omitted 2021-22.
How to handle overenrollment: Preference is given to first and second year students, with a mix of math majors and non-majors.
Students who enroll in this course will likely encounter and be expected to engage in the following intellectual skills, modes of learning, and assessment: Individual and group projects, Problem sets, Short writing assignments, Regular reading assignments.
M 01:00 PM - 01:50 PM SMUD 206
Tu 01:00 PM - 02:20 PM SMUD 207
Th 01:00 PM - 02:20 PM SMUD 207
|All||Gaming the Vote||Hill & Wang||Poundstone||TBD|
|All||Numbers Rule: The Vexing Mathematics of Democracy||Princeton||Szpiro||Free E-book||TBD|
|All||The Mathematics of Voting and Elections: A Hands-On Approach Second Edition 2018||Hodge and Klima||Free E-book||TBD|