HSEM2512H: The Mathematics of Elections and Social Choice

This course will focus on the mathematics behind Voting Theory, apportionment, and fair division. Whether it is choosing a student association representative or ranking NCAA sports teams, there are a variety of selection methods that could be employed, but which is best? This course will use mathematics to study the strengths and weaknesses of different ways to tally votes or hold an election. Voting methods to be studied include single ballot vs instant-runoff (also known as a ranked-choice), as well as point-based rankings. This course will also explore the mathematics behind apportionment (and how it can lead to paradoxes), and how mathematics is used to evaluate the fairness of congressional districts in the context of gerrymandering. Finally, we will investigate ways to measure power differences between coalitions, and how to approach problems of fair-division like rent-sharing.

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