Mathematical Moments From The American Mathematical Society

As difficult as it is to do the census, the ensuing process of determining the number of congressional seats for each state can be even harder. The basic premise, that the proportion of each state's delegation in the House should match its proportion of the U.S. population, is simple enough. The difficulty arises when deciding what to do with the fractions that inevitably arise (e.g., New York can't have 28.7 seats). Over the past 200 years, several methods of apportioning seats have been used. Many sound good but can lead to paradoxes, such as an increase in the total number of House seats actually resulting in a reduction of a state's delegation. The method used since the 1940s, whose leading proponent was a mathematician, is one that avoids such paradoxes. A natural question is Why 435 seats? Nothing in the Constitution mandates this number, although there is a prohibition against having more than one seat per 30,000 people. One model, based on the need for legislators to communicate with their constituent