Hamilton Method?

Question

Given the cities and the populations below, use the hamilton method of apportionment to distribute 25 seats on a regional board.
City POP
Greenville 34,569
riverdale 27,943
oceanview 21,350
parkview 16,138

Answer 1

Alexander Hamilton proposed a method of dividing votes, or seats on a board based on population. Hamilton's method was adopted by the US Congress in 1852 and was in use through 1911 when it was replaced by Webster's method.

A given number of seats (25 in your example) is to be apportioned between several cities (4) proportionally to their populations. To accomplish that task according to Hamilton:

Compute the divisor D = (Total population)/(Number of seats)
D = 100,000 / 25 = 4,000

Find and round down city seats {(City population)/D}. The leftover fractional parts add up to a whole number of seats.
Distribute the surplus seats, one per state, starting with the largest leftover fractional part, then proceeding to the next largest, and so on, until all the surplus seats have been dealt with.

In your example, your total population is 100,000 (add up the 4 cities). That means you should get 1 seat for 4,000 people (100,000 / 25).

Greenville gets 8 (8 * 4000 = 32,000 with 2,569 left over)
Riverdale gets 6 (6 * 4000 = 24,000 with 3,943 left over)
Oceanview gets 5 (5 * 4000 = 20,000 with 1,350 left over)
Parkview gets 4 (4 * 4000 = 16,000 with 138 left over).

That's 23 seats allocated. Looking at the remainders, Riverdale and Greenvale should each get one extra seat.

So the final apportionment is:
Greenville gets 9
Riverdale gets 7
Oceanview gets 5
Parkview gets 4