# Huntington-Hill Apportionment Method

Huntington-Hill's method is the current method of seat apportionment used by the US Congress. It has been signed in law by President Roosevelt on November 15, 1941.

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The given total number of seats (23 in the applet) is to be apportioned between several (3 at the ouset) states *proportionally* to their populations. To accomplish that task according to Huntington-Hill,

- Compute the divisor D = (Total population)/(Number of seats)
- Modify D by an amount d, that could be negative, such that when state allocations
{(State population)/(D + d)} are rounded according to the*method of equal proportions*, they add up to the exact number of seats.

With the regular rounding used in the Webster's method the cutoff value is midway between two successive integers. If A is between an integer L and the next integer L+1, then it is rounded down or up depending on whether A is less or greater than the average

In the *method of equal proportions*, the cutoff value depends on the magnitude of

(One of the applets at this site combines the Huntington-Hill and four additional methods of apportionment under a single umbrella.)

### Reference

*For All Practical Purposes*by COMAP, 5^{th}edition, W. H. Freeman & Company, 2008 (8th edition)- G. Szpiro,
*Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present*, Princeton University Press, 2010. - P. Tannebaum & R. Arnold,
*Excursions In Modern Mathematics*, 7th edition, Prentice Hall, 2009

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Copyright © 1996-2018 Alexander Bogomolny

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