By Eric Bergman and Huma Syed/reporters
Fair Representation: The Mathematics of Apportionment gave SE students a background and understanding for the democratic way of how the electoral process functions.
Dr. Rhonda Hatcher, TCU math professor since 1990, presented the apportionment seminar April 9.
Hatcher defined apportionment as the methodology and science behind the distribution of votes.
Although 435 House members cover the 50 U.S. states, Hatcher said the distribution is not even as it depends on the population density of each state. This distribution changes every 10 years, but the total number remains 435.
“Currently there are 281,421,906 people living in the United States,” she said.
This number approximates to 646,947 people for each of the members. Hatcher said the 646,947 is the representative figure for the “natural divisor,” found by dividing the total population by the size of the house.
Hatcher explained how the system works by using Texas.
“Texas’ natural quota is 32.23 seats,” she said.
Rounding comes into play because there obviously cannot be a fraction of a seat. Hatcher said the system does not always work because the math is not 100 percent accurate when dealing with rounding. The Constitution does not specify a formula for the apportionment method.
Over time, Hatcher said five methods of apportionment have been used in calculating the number of seats in a state, each named for its originator: Hamilton’s Method, Lowndes’ Method, Jefferson’s Method, Webster’s Method and the one used today—Hill-Huntington Method.
Each method is done by attaining a national quota, modified quota and a final allocation. The seats are then determined by adding up the final allocation.
“Alexander Hamilton [in 1791] suggested that all states be rounded down and to give the others away according to their fractions,” she said.
The idea was sound, yet George Washington used the first veto in history to stop it, and the United States opted to use Thomas Jefferson’s idea until 1841, Hatcher said. Jefferson’s Method was the divisor method, which Hatcher said benefits larger states more than smaller ones.
Webster’s method was adopted in 1842 and was in place through 1851. Hatcher said Webster’s system was simple, rounding to the nearest whole number. Since this system rounds up and down, it does not favor a large or small state.
Yet during that time another idea had come to light and “was almost adopted from William Lowndes of South Carolina,” she said. “It was nothing more than another version of Hamilton’s idea with more stress upon the largest relative fraction and initial allocation.”
Hatcher said a bizarre turn of events occurred when Hamilton’s method was adopted from 1852-1900,” she said.
Then in the 20th century, official methods changed several more times.
“1901 went back to Webster’s method,” she said. “Then in 1911, the chief of statistics at the Bureau of the Census, Joseph Hill, devised a new, yet highly complex method.”
Hill and fellow professional Edward V. Huntington from Harvard perfected this system in the 1920s, Hatcher said. In 1941, it became known as the Hill-Huntington Method, which uses the common mathematical formula for finding the geometric mean. It proposed that as “n” gets larger, the cutoff point for rounding gets larger as well. This method turned out to be the same as Webster’s Method.
“A theorem was devised in 1982 by Balinski and Young that no method satisfies all issues between the quota property, house size property and population property,” she said.
The problem here is that as the house size goes up, the state can lose a seat.
This is true when Hamilton’s Method is applied.
“The one flaw that should not be cared about today is House-size property,” she said.
As far as mathematicians go, Hatcher said Webster’s Method is favored the most because it does not violate the divisor method.
“These are not always a fair representation in terms of elections, but the president does get elected by an electoral college, and each state gets two seats for the Senate,” she said.
But, Hatcher said, apportionment does matter. For instance, the 1876 presidential election was decided by a single electoral vote.
“Two seats that went to New Hampshire and Florida by the apportionment method used at the time would have gone to New York and Illinois,” she said.
That shift would have made Samuel Tilden president over Rutherford B. Hayes.
“Hamilton’s method would have made a difference,” she said. “Every vote counts.”
Hatcher has won multiple awards and co-authored many books on the subject.
“I wish I had this many students from the TCU campus come,” she said.
For further information regarding apportionment, Hatcher suggested Fair Representation by Michael L Balinski and H. Peyton Young.
