Hamilton Method

The Hamilton method (also known as the Hare-Niemeyer method, Vinton's method, or the largest remainder method) is a method of apportionment. The name Hamilton method is used here, since Alexander Hamilton proposed the method for apportioning the House of Representatives in 1792.

The Hamilton method first assigns seats to those that have a whole number value for needing a seat, then assigning seats to those with the largest fractional remainder.

The following example is given:

Assume Alabama has a population of 398,000 (P = 398,000), Alaska has a population of 400,000 (P = 400,000), and Arkansas has a population of 230,000, and a divisor of 90,000 (D = 90,000) is chosen. Since there are 1.028 million people, the legislator allows 12 seats to be assigned.

First determine the amount of seats each state should theoretically get:

Alabama: 398,000 / 90,000 = 4.42

Alaska: 400,000 / 90,000 = 4.44

Arkansas: 230,000 / 90,000 = 2.56

First seats are awarded by whole number seats, so Alabama and Alaska each receive 4 seats while Arkansas receives 2 seats.

Then seats are awarded based on states with the largest fraction. Thus Arkansas receives its third seat and then Alaska receives a fifth seat. All twelve seats are now allocated.