1793Following the 1790 Census, Congress apportioned the House of Representatives for the first time. This apportionment was first used for election of the Third Congress, whose term began on March 4, 1793 (elections were held from August 1792 through September 1793), as well as determining the number of electors for the second presidential election in 1792.
In this model, Congress decided to base the number of representatives on the
cube root rule, but limiting the rate of increase to no more than 15% per decade. Direct application of the cube root rule would have results in a House of 157 representatives, more than doubling the size after just four years. It would have also violated the limit in the Constitution of at least 30,000 persons per representative (157 members would have averaged 24,800 persons). I have ignore the 3/5 rule in these calculations.
So beginning with 70 members, the increase was limited to 15% or a maximum of 80 members.
Representatives were apportioned using
Adams method. Under Adams method, a state's population is divided by a quota, and the resulting quotient is rounded up to the next larger whole number (i.e. ceiling). This ensures that the average population per representative for any state is less than the quota. The quota is in effect a cap on district population - if representatives are elected by single member districts.
Adams method may be applied directly using the quota, or using a priority list, where the divisor for a State's 3rd representative is 2, for the 4th representative is 3, for a n
th representative n-1. Either calculation produces the same result. I use the quota since it provides the quality of a maximum number of persons per representative.
In practice, there might be experimentation (e.g. if I use a quota of 40,000 how large would the House be?) The same could be done with the priority list method, there is no reason that priority for a 433rd, 434th, 435th, 436th, 437th representative could not be calculated, and then the size of the House decided. This would likely be a political decision. If your state was 437, you would argue for a larger House. If the next decade you were 433, you would argue that the larger House had proven itself unworkable.
What I did was first choose the target size, then adjust the quota to the smallest multiple of 1000, such that the number of apportioned representatives was less than or equal to the target. This produces a nice round quota, and may slightly lessen the chance a split where two states are virtually tied.
The US population in 1790 was 3,893,523. Under the cube root rule this would result in a House of 157(.32) members, more than doubling the existing size of 70. 115% of 70 is 80(.50). The target size is 80.
A quota of 53000 would have resulted in 82 members, a quota of 55000 would result in 79. The final quota of 54000 results in 80 members. In real life, the House had 105 members.
The new apportionment results in the following changes. The large increases for Virginia and North Carolina are in part due to ignoring the 3/5 rule.
Virginia | +5 |
North Carolina | +3 |
Massachusetts | +1 |
New York | +1 |
Pennsylvania | +1 |
Georgia | -1 |
Dark Green states, VA(+5), and NC(+3) gained multiple representatives. Light green states, MA, NY, and PA increased by one representative. ME is part of MA, its share of the 9 representatives would be 2, one more than its 1/8 share that Massachusetts had allocated to it under the Constitution.
States in pink, GA lost a representative. This suggests that the estimate use for the Constitution had been too high.
States in yellow have no change.
States with two representatives, DE, GA, KY, RI, and VT, earned them under Adams method - they each had a population greater than the quota of 54,000 but less than two quotas or 108,000. There was no need for application of Madison's rule (but it is possible that the Adams method might have been chosen for that reason).