The Hamilton/Vinton Method
The Hamilton/Vinton Method sets the divisor as the proportion of the total population per house seat. After each state's population is divided by the divisor, the whole number of the quotient is kept and the fraction dropped. This will result in surplus house seats. The first surplus seat is assigned to the state with the largest fraction after the original division. The next is assigned to the state with the second-largest fraction and so on.For example:
If a country had 4 states, and a 20-seat House of Representatives...
2560 + 3315 + 995 + 5012 = 11882
11882 ⁄ 20 = 594.1
State Population Quotient First Allocation of Seats Left Over Decimal Seats Apportioned
A 2560 2560 ⁄ 594.1 = 4.31 4 .31 4
B 3315 3315 ⁄ 594.1 = 5.58 5 .58 6
C 995 995 ⁄ 594.1 = 1.67 1 .67 2
D 5012 5012 ⁄ 594.1 = 8.44 8 .44 8
Total = 20 Seats
31 58 67 44
To understand the Hamilton/Vinton Method of apportionment, we can follow these steps:
1. Calculate the total population of all the states. In this example, the total population is 11882.
2. Determine the number of seats in the House of Representatives. In this case, there are 20 seats.
3. Calculate the divisor. The divisor is found by dividing the total population by the number of seats: 11882 ÷ 20 = 594.1
4. Divide each state's population by the divisor to find the quotient. Round down to the nearest whole number and ignore the decimal fraction. This gives us the initial allocation of seats for each state.
- For State A: 2560 ÷ 594.1 = 4.31, round down to 4.
- For State B: 3315 ÷ 594.1 = 5.58, round down to 5.
- For State C: 995 ÷ 594.1 = 1.67, round down to 1.
- For State D: 5012 ÷ 594.1 = 8.44, round down to 8.
5. Calculate the decimal fraction leftover for each state by subtracting the whole number allocation from the quotient. This represents the fraction of a seat that each state still needs.
- For State A: 4.31 - 4 = 0.31
- For State B: 5.58 - 5 = 0.58
- For State C: 1.67 - 1 = 0.67
- For State D: 8.44 - 8 = 0.44
6. Assign the surplus seats based on the largest leftover decimal fraction. Start by awarding the surplus seat to the state with the largest fraction, then continue assigning seats to states with the next largest fractions until all surplus seats are allocated.
- The first surplus seat goes to State B with a leftover fraction of 0.58, increasing its allocation from 5 to 6.
- The second surplus seat goes to State D with a leftover fraction of 0.44, increasing its allocation from 8 to 9.
7. Sum up the total number of seats allocated to all the states. In this case, the total is 20, which matches the given number of seats.
The Hamilton/Vinton Method uses a divisor based on the proportion of the total population per seat to allocate seats to each state. It ensures that larger states receive more seats but also accounts for their fractional population to distribute the surplus seats.