Hamilton method
The Hamilton method (or Largest Remainder-Hare/LR-Hare) 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[edit | edit source]
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 |
Extensions of theory[edit | edit source]
Several cardinal PR methods reduce to Hamilton if certain divisors are used. Some of which are:
Notes[edit | edit source]
Hamilton doesn't guarantee that a majority of voters will always win at least half of the seats (though LR-Hagenbach-Bischoff does, since a majority always has more votes than a majority of Hagenbach-Bischoff quotas).
Votes | Votes % | Fraction | Automatic seats | Remainders | Additional seats | Final seats | Seats % | |
---|---|---|---|---|---|---|---|---|
A | 503 | 50.3% | 17.605 | 17 | 0.605 | 17 | 48.57% | |
B | 304 | 30.4% | 10.640 | 10 | 0.640 | +1 | 11 | 31.43% |
C | 193 | 19.3% | 6.755 | 6 | 0.755 | +1 | 7 | 20% |
Total seats awarded | 33 | +2 | 35 |
Party A, with 50.3% of the votes, only gets 17 out of 35 seats, which is 48.57% of the seats, a minority.[1]
See also[edit | edit source]
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- ↑ "ELECTION INVERSIONS UNDER PROPORTIONAL REPRESENTATION" (PDF). p. 16. line feed character in
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at position 20 (help)