Geometric Mean and Huntington–Hill Method The method currently being used to appo...

Geometric Mean and Huntington–Hill Method

The method currently being used to apportion the U.S. House of Representatives is the Huntington–Hill method, which has been the official apportionment method since 1941. It is a variation of Webster’s method but differs from it in that the decision to round a modified quota is based on whether the modified quota is less than or greater than the geometric mean of the two whole numbers immediately before and after it. The geometric mean of two numbers differs from the arithmetic mean, or “average” of the two numbers. The geometric mean of two whole numbers, a and b, is Under the Huntington–Hill method, if the modified quota is greater than the geometric mean of the whole numbers just above and below it, the modified quota is rounded up to obtain the number of seats. If the modified quota is less than the geometric mean of those two numbers, it is rounded down.

For example, in applying the Huntington–Hill method, suppose that the modified quota under consideration is 4.475. The whole number less than 4.475 is 4, and the whole number greater than 4.475 is 5. The geometric mean of a = 4 and b = 5 is Because 4.475 is greater than 4.4721, the modified quota is rounded up to 5. If the modified quota under consideration had been 5.475, the geometric mean of 5 and 6 would have been In this case, the modified quota would have been rounded down to 5, since 5.475 < 5.4772.

A paradox of the Huntington–Hill method is that two states can have quotas that differ by more than 1 yet have the same apportionment. Create an apportionment example that illustrates this phenomenon.