## Divvying up the House

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This news article today on nature.com discusses the mathematics of divvying up seats in the House of Representatives. There are 435 seats in the House, which are allocated according to the population of each state. But there’s a problem: using a strict proportion would leave states with fractional seats. According to the 2000 Census, New York State had an official population of 18,976,457 and the United States had a population of 281,421,906, which would give New York (18,976,457/281,421,906) of the 435 seats, or 29.33 seats. Rounding down gives 29 Representatives, which New York in fact has, but simple rounding state-by-state could lead to a total that is actually different from 435. [Hmmm….how different could it be above or below? That’s an interesting question — anyone know?]

But I digress…the article above describes the mathematical methods that have been used in the past to address this issue, such as rounding those with the biggest difference first, or rounding up or down from different points (for a number between 29 and 30, for example, the cutoff in one case is the geometric mean √(29·30)≈29.4958 instead of the arithmetic mean of 29.5). It goes on to describe a proposal by Paul Edelman, a mathematician and law professor at Vanderbilt University, which may be fairer to small states. (But may be unfair to large ones, according to other parts of the article.) All in all, an interesting read and an interesting math problem!

Cool aside: Dr. Edelman presented this information at the 2008 Joint Mathematics Meetings in San Diego on Sunday night!