The History of Apportionment: The Process Which Determines the Number of House Seats per State
Gerrymandering is a hot topic in our current political discourse. However, gerrymandering has not always been the preferred method of manipulating the House of Representatives without worrying about pesky voters. Since the founding of America until FDR, apportionment, the process which determines the number of House seats a state has based on population, has been an issue of contention. It may seem as if it is easy to determine how many House seats each state should get, but it is not. The first apportionment is directly laid out in the Constitution, but after the first census in 1790, the infighting began.
Hamilton vs. Jefferson
Initially, two main methods of apportionment emerged: Hamilton’s method and Jefferson’s method. The first step in both methods involves determining how many citizens should be presented by one House member by dividing the total population of the U.S. by the predetermined number of total House seats. Next, per both methods, the ideal number of representatives per each state is calculated by dividing the population of that state by the number of citizens to be represented by each House member. Because this will likely lead to fractions of representatives, both Hamilton and Jefferson suggested rounding down to the nearest whole number. At this point, there will be too few overall representatives, and Hamilton and Jefferson differed as to how the additional representatives should be allocated. Hamilton suggested adding additional representatives based upon the relative size of remainders, while Jefferson suggested decreasing the number of people each representative represents until the total number of representatives equals the predetermined number.
For example, let’s assume a three state country with a total population of 10,000,000 and 10 seats. In this scenario, each representative should represent 10,000,000/10 = 1,000,000 citizens. If the total citizens were spread across the three states as indicated below, the resulting first pass number of representatives per state would be as follows:
Because representatives cannot be fractions of people, both Hamilton and Jefferson suggested each state round down the number of representatives to the nearest whole number:
Since rounding down results in too few representatives, Hamilton suggested the additional representatives (two in this case) are allocated to each state based upon their relative remainder. State A receives the first additional representative, as its remainder is .9, and State C receives the second additional representative, as its remainder is .6. Therefore, the final allocation of House seats is as follows:
Jefferson’s method mimics Hamilton’s method, except for the final step. Instead of adding additional seats based upon the relative size of the remainders, Jefferson suggested decreasing the number of people each representative represents (rounding down along the way) until the total number of representatives equals the predetermined number.
Assuming the same example as above, Hamilton’s and Jefferson’s method look the same up until this point:
At this juncture, Jefferson suggested decreasing the number of citizens each representatives represents until the desired effect is achieved. For example, if the number of citizens per representative is decreased from 1M to 900K, the result is as follows:
Adams’ Method
During this time a different New Yorker came up with another apportionment method to benefit the Empire State. John Adams proposed a method which is the exact same as Jefferson’s method, except it involves rounding up (which leads to too many representatives in total) and then increasing the number of people each representative represents in order to achieve the desired result.
Assuming the same set of facts, and increasing the number of people represented per seat from 1M to 1.15M, Adam’s method works as followings:
The fact that Hamilton’s and Adams’ methods in the examples above yield the the same number of representatives is a coincidence due to the simple nature of my assumptions, although both Hamilton’s and Adam’s methods tend to benefit smaller states, while Jefferson’s method tends to benefit larger states, and at the time these methods were initially proposed, New York was smaller than Virginia.
So whose method prevailed? The U.S. originally decided to use Jefferson’s method (Washington used his first veto to reject Hamilton’s method on the basis that it was unconstitutional) and the U.S. continued to use Jefferson’s method until the 1830 census.
Webster’s Method
For the appointment after the 1830 census, both sides met in the middle and decided to round to the nearest whole number and adjust the number of people per representative as needed. This is referred to as Webster’s method.
Continuing with the same set of facts, Webster’s method would result in the following apportionment of House seats:
The first pass at rounding to the nearest whole number led to a total of 11 seats, which is why the number of citizens per representative was increased (in this example, from 1M to 1.03M) so that the second pass at rounding to the nearest whole number led to a total of 10 seats. Given a different numeric example, it could have been the case that the first pass at rounding to the nearest whole number led to a total number of seats less than 10, in which case the number of citizens per representative would have been decreased to achieve the desired overall result of 10 seats.
Webster’s method only lasted for 20 years because Hamilton’s method came back and was used from approximately 1852 to 1912 (the next six censuses). During this period the U.S. grew rapidly, which exposed many flaws in Hamilton’s method. In particular, during the 1880 census the addition of new states led to more total House seats. When testing out how many seats should be added under Hamilton’s method, using a total of 299 seats, Alabama was allocated eight seats; however, using a total of 300 seats, Alabama was allocated seven seats. This is referred to as the Alabama paradox. Another flaw of Hamilton’s method is referred to as the Oklahoma paradox. When Oklahoma became a state in 1907, new seats were added to the House; consequently, New York lost a seat and Maine gained one. For these reasons and more, the U.S. switched back to Webster’s method (again) after the 1910 census, thus Hamilton’s method was last reflected in the 1912 House.
Hill’s Method
The apportionment was changed one last time in 1941 to a method that is very similar to Webster’s method but always ensures any state, no matter how small, will get at least one House seat. The method is referred to as the Hill’s method. Hill’s method involves rounding based upon the geometric mean, as opposed to the arithmetic mean. A geometric mean is the square root of the product of two numbers. Using the geometric mean, as long as your population is greater than zero, you round up to at least one seat. There are other differences between arithmetic and geometric means as well; however, as numbers increase, the differences between the arithmetic mean and geometric mean decrease. Hill’s method, like every other apportionment change, was not made out of any moral argument, but instead, a political one. At the time, the Democrats had a trifecta and had supermajority in the Senate. Because of this power, they passed a bill changing the apportionment method from Webster’s method to Hill’s method because the only difference between the two methods was Hill’s method gave an extra seat to Arkansas, a loyal Democratic state (at the time), and took one away from Michigan, which was more of a swing state.
Today
We have stuck with Hill’s method since 1941 because the Democrats held power for another 12 years and then no one has bothered to change it. And besides, Hill’s method is just fine in every non-extreme case. So when you hear someone bickering about how gerrymandering has ruined modern day politics, just know this sort of bickering goes back to the founding of our nation between Hamilton and Jefferson and is about as American as you can get.
