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

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.

The first apportionment of the U.S. House of Representatives was calculated using Jefferson’s method. Use the information that follows to determine if the apportionment would have changed if the Huntington–Hill method had been used instead. The 1790 apportionment population totals are given in problem 17 of section 5.2. Use the Huntington– Hill method to reapportion the 105 house seats in 1790. Compare your results with those obtained under Jefferson’s method in problem 17 of section 5.2 and those obtained under Hamilton’s method in problem 15 of section 5.1. How are the apportionments different?

Problem 15 or 17:

In 1791, Thomas Jefferson helped to convince President George Washington to veto a bill that established a 120-member House of Representatives to be apportioned using Hamilton’s method. When the House could not override Washington’s veto, a new bill was passed that established a 105-member House to be apportioned using Jefferson’s method. In 1800, there were 141 seats in the House. The following table contains apportionment population totals for the states that were part of the United States in the years 1790 and 1800.