Assigning Seats - Part 1

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 constituents and with each
other, uses algebra and calculus to show that the ideal assembly
size is the cube root of the population it represents. Remarkably,
the size of the House mirrored this rule until the early 1900s. To
obey the rule now would require an increase to 670, which would
presumably both better represent the population and increase the
chances that the audience in the seats for those late speeches
would outnumber the speaker. For More Information: "E pluribus
confusion", Barry Cipra, American Scientist, July-August 2010.