Fair Shares? The Mathematics of Political Apportionment by Jaskaran Singh & Kunal Pal '25

Fair Shares? The Mathematics of Political Apportionment by Jaskaran Singh & Kunal Pal ’25, Wednesday February 19, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Colloquium

Abstract: How do we fairly divide seats in a legislature among different states based on population? The problem of apportionment has shaped political systems for centuries leading to surprising results. In this talk, we will explore the history and mathematics behind different apportionment methods, from Jefferson’s and Hamilton’s methods to modern divisor methods. We will examine key theorems that govern apportionment, including Balinski and Young’s Impossibility Theorem, which proves that no method can satisfy all fairness criteria simultaneously. Along the way, we will uncover the mathematical paradoxes that influence political representation, such as the Alabama Paradox. This talk will illustrate the power and limitations of mathematics in shaping democratic institutions.