# 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.

(Bold numbers could be clicked upon. To increase the number, click to the right of its vertical center line. To decrease it click to the left of the line. Dragging the mouse near the center line will accomplish the same task, but faster.)

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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,

1. Compute the divisor D = (Total population)/(Number of seats)
2. 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 (L + (L+1))/2.

In the method of equal proportions, the cutoff value depends on the magnitude of L = [A] and is equal to the square root of L(L+1).

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

### Reference

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

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