Jefferson method
Jefferson's method was used to apportion the U.S. House of Representatives between 1792 and 1840.
Procedure
Choose a divisor D. A state with population N (or a political party with N seats) is entitled to floor(N/D) seats. If the number of seats allocated equals the size of the legislative body, then use the apportionment just calculated. Otherwise, choose a new value for D and try again.
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.
If a divisor of 55 000 is used, the resulting apportionment is
| State | Quotas | Seats | District size | Rel. rep. |
|---|---|---|---|---|
| Virginia | 11.46 | 11 | 57 324 | 1.0513 |
| Massachusetts | 8.64 | 8 | 59 416 | 1.0143 |
| Pennsylvania | 7.87 | 7 | 61 840 | 0.9745 |
| North Carolina | 6.43 | 6 | 58 920 | 1.0228 |
| New York | 6.03 | 6 | 55 265 | 1.0905 |
| Maryland | 5.06 | 5 | 55 703 | 1.0819 |
| Connecticut | 4.31 | 4 | 59 210 | 1.0178 |
| South Carolina | 3.75 | 3 | 68 745 | 0.8766 |
| New Jersey | 3.26 | 3 | 59 857 | 1.0068 |
| New Hampshire | 2.58 | 2 | 70 911 | 0.8499 |
| Vermont | 1.56 | 1 | 85 533 | 0.7046 |
| Georgia | 1.29 | 1 | 70 835 | 0.8508 |
| Kentucky | 1.25 | 1 | 68 705 | 0.8772 |
| Rhode Island | 1.24 | 1 | 68 446 | 0.8805 |
| Delaware | 1.01 | 1 | 55 540 | 1.0851 |
| Total | 65.74 | 60 |