Hamilton method
The Hamilton method is a version of the largest remainder method for allocating seats proportionally for representative assemblies with party list voting systems. It uses the Hare quota as the initial quota.
Example
In 1790, the U.S. had 15 states. For the purpose of allocating seats in the House of Representatives, the state populations were as follows:
| State | Population |
|---|---|
| Virginia | 630 560 |
| Massachusetts | 475 327 |
| Pennsylvania | 432 879 |
| North Carolina | 353 523 |
| New York | 331 589 |
| Maryland | 278 514 |
| Connecticut | 236 841 |
| South Carolina | 206 236 |
| New Jersey | 179 570 |
| New Hampshire | 141 822 |
| Vermont | 85 533 |
| Georgia | 70 835 |
| Kentucky | 68 705 |
| Rhode Island | 68 446 |
| Delaware | 55 540 |
| Total | 3 615 920 |
Suppose that there were to be 60 seats in the House.
The quota is 3 615 920 ÷ 60 = 60 265.333. Dividing the state populations by the quota gives
| State | Quotient | Remainder |
|---|---|---|
| Virginia | 10 | 27 906.7 |
| Massachusetts | 7 | 53 469.7 |
| Pennsylvania | 7 | 11 021.7 |
| North Carolina | 5 | 52 196.3 |
| New York | 5 | 30 262.3 |
| Maryland | 4 | 37 452.7 |
| Connecticut | 3 | 56 045.0 |
| South Carolina | 3 | 25 440.0 |
| New Jersey | 2 | 59 039.3 |
| New Hampshire | 2 | 21 291.3 |
| Vermont | 1 | 25 267.7 |
| Georgia | 1 | 10 569.7 |
| Kentucky | 1 | 8 439.7 |
| Rhode Island | 1 | 8 180.7 |
| Delaware | 0 | 55 540.0 |
| Total | 52 |
Each state receives a number of seats equal to the integer part of the quotient. The remaining 8 seats are given to the states with the largest remainders: New Jersey, Connecticut, Delaware, Massachusetts, North Carolina, Maryland, New York, and Virginia. The final apportionment is:
| State | Seats | District size | Rel. rep. |
|---|---|---|---|
| Virginia | 11 | 57 324 | 1.0513 |
| Massachusetts | 8 | 59 416 | 1.0143 |
| Pennsylvania | 7 | 61 840 | 0.9745 |
| North Carolina | 6 | 58 920 | 1.0228 |
| New York | 6 | 55 265 | 1.0905 |
| Maryland | 5 | 55 703 | 1.0819 |
| Connecticut | 4 | 59 210 | 1.0178 |
| South Carolina | 3 | 68 745 | 0.8766 |
| New Jersey | 3 | 59 857 | 1.0068 |
| New Hampshire | 2 | 70 911 | 0.8499 |
| Vermont | 1 | 85 533 | 0.7046 |
| Georgia | 1 | 70 835 | 0.8562 |
| Kentucky | 1 | 68 705 | 0.8772 |
| Rhode Island | 1 | 68 446 | 0.8805 |
| Delaware | 1 | 55 540 | 1.0851 |
| Total | 60 |