Events

Event Description

David McCune, professor of mathematics at William Jewell College, presents "The mathematics of apportionment paradoxes in presidential primaries."

In rare circumstances, a candidate in a presidential primary can gain delegates while losing votes. This talk explores the mathematics behind these paradoxes, with examples from recent presidential primaries. Apportionment theory traces its origin to the U.S. Constitution, which stipulates that seats in the U.S. House be apportioned to states in proportion to their population — a principle that is intuitively simple but hard to implement, since seats cannot be divided.

If a state has 10% of the country's population, it should receive 10% of the seats in the House. This is the apportionment problem: how to distribute indivisible goods such as House seats among entities such as states in proportion to their population. Historically, the seemingly straightforward question of how to round these fractions has generated considerable controversy.

A similar problem arises in state party presidential primaries, where delegates are apportioned to candidates in proportion to their vote totals. The methods used to solve it can produce surprising and even paradoxical outcomes.