The Mathematics of Elections, Fairness, and Representation (26w5503)

The Banff International Research Station will host the "The Mathematics of Elections, Fairness, and Representation" workshop in Banff from March 29 - April 3, 2026.

This workshop explores problems in mathematical political science, focusing on recent developments in the study of alternative voting methods and the creation of district electoral maps. Over the last 20 years, many jurisdictions in Canada and the United States have adopted or have considered adopting alternative voting methods such as ranked-choice voting for electing mayors, representatives, city council members, etc. There are many questions about such methods which can be analyzed mathematically. For example, does ranked-choice voting tend to elect candidates who are more centrist than candidates elected by more commonly-used methods like plurality? How can we best achieve proportional representation on a legislative body? What makes an election fair? There are many open problems around such questions, and this workshop hopes to make some progress on them using mathematical tools.

Additionally, a given election occurs in a specific geographical region, and the way such regions are chosen can have a large effect on electoral outcomes. This workshop also examines the criteria for drawing fair electoral maps. This area of study is particularly relevant in the United States, where congressional and state legislative districts are redrawn every ten years, or more frequently if maps are legally challenged for perceived unfairness. Since the 2010 U.S. Census, there has been a substantial increase in interest within the mathematical community regarding fair districting. This workshop seeks to capitalize on this momentum to advance research in this field.