Vanderbilt Lawyer - Volume 37, Number 1

Getting the Math Right

Paul Edelman has developed a system for congressional reapportionment that comes closer to the 'one man, one vote' ideal.

by Grace Renshaw Professor Paul Edelman

Paul Edelman was teaching a new course entitled "Social Choice, Fairness and the Law" in spring 2001 when he realized the Supreme Court had made a mathematical error in its decision in a 1992 case, U.S. Department of Congress v. Montana. His quest to determine whether that error had an impact on the Court's decision in the case ultimately led him to propose a new apportionment method.

Edelman was teaching Montana, a case brought in 1991 after the state lost its second congressional seat due to reapportionment, because "I wanted the class to think about how you measure representation." As he researched cases that addressed the 'one man, one vote' issue while developing the course, Edelman had discovered that "Montana is the only opinion the Court has issued on the mechanics of apportionment, and in that case, the Court deferred to Congress, because unlike congressional districting, it could not find a single workable measure for apportionment." His lesson plan involved working with his students to reconstruct the math upon which the Montana decision was based. "But when we did the math on the board in class, we got different answers than the Court," Edelman says. "It turned out that the reason the Court couldn't find such a measure was that it made a math error in its decision."

Edelman, who holds a Ph.D. in mathematics from MIT and is a professor of mathematics at Vanderbilt as well as a professor of law, was taken aback by his discovery. "I didn't expect to find out that the Supreme Court had made a math error in an important decision," he admits. But he was also confident his results were correct. His realization that "there was something wrong with the way we do apportionment" piqued his interest in the method used to determine the number of congressional representatives allocated to each state - a number that also determines each state's number of electoral votes. "When the Court got the numbers wrong, it materially affected what they could then say," he says. "I wanted to figure out why the Court got it wrong and how they got the numbers they got."

Edelman spent the next two years researching case law relating to congressional apportionments. "The Constitution simply states that the seats in the House of Representatives must be apportioned among the states according to the population, which sets the stage for a recurring struggle every 10 years," he says. States that lose a representative often challenge the census results in court, as Utah did in 2001 after it lost a House seat to North Carolina. The Supreme Court refused to hear two different versions of Utah's case, in which the state claimed that the 2000 census had failed to account for a large number of Mormon missionaries temporarily living abroad while crediting North Carolina for its large population of military personnel living abroad.

However, these cases dealt primarily with census processes and results, while the crux of the problem, according to Edelman, is that "the Constitution doesn't specify the method used to apportion those seats except to command that each state have at least one representative."

Indeed, developing a method that insures a fair allocation of congressional representation has proven so problematic that three different apportionment methods, developed by Alexander Hamilton, Thomas Jefferson and Daniel Webster, were used before the current method, developed by a U.S. Census Bureau statistician, Joseph A. Hill, was adopted in 1941. Two other methods developed in the 1800s by John Quincy Adams and a physics professor, James Dean, have also factored into the ongoing debate about which method yields a result that comes closest to achieving the democratic ideal of 'one man, one vote.'  "Each of these methods can produce different results," Edelman says, "and methods favorable to certain states inevitably come up when that state isn't happy with the results of a reapportionment."

Edelman found the legal logic he was searching for when he began reviewing Supreme Court rulings in Congressional districting cases. "These cases deal with an issue that's very similar to congressional apportionment," he says. Edelman concluded that "the Court clearly prefers a method that minimizes deviation in the size of Congressional districts." The new apportionment method he has developed, which is designed to yield the closest possible mathematical result to the 'one man, one vote' ideal, is based on the precedents established in these cases.

Edelman laid out the legal precedents underlying his method in "Getting the Math Right: Why California Has Too Many Seats in the House of Representatives," a 2006 Vanderbilt Law Review article. Thanks to the presidential primaries, his proposal began to garner attention in January 2008, when he presented the algorithm he developed to calculate the apportionment, a method he calls the Minimum Total Deviation (MTD), in an invited address at a major annual conference of mathematics scholars in San Diego. The Wall Street Journal's "Numbers Guy" columnist, Carl Bialik, was in the audience, and after the Pennsylvania primary in April, when it became evident that the number of electoral votes allocated to each state was likely to have a big impact on the choice of a Democratic presidential nominee, Bialik featured Edelman's MTD method prominently in his column, along with charts showing how each state would fare under every apportionment method.

Edelman concedes that the MTD method favors smaller states. "The number of Congressional districts is fixed at 435," he explains. "The method I propose would distribute Congressional seats in a way that minimizes the difference between the number of people in the largest districts and those in the smallest, and the results of that calculation tend to favor less populous states, which already have fewer representatives." Had Edelman's MTD calculations been used following the 2000 census rather than the Hill method, California would have lost three representatives, and Florida, New York, North Carolina, Ohio and Texas would each have lost one. The states of Connecticut, Delaware, Mississippi, Montana, Oklahoma, Oregon, South Dakota and Utah would each have gained one representative.

"Each state's electoral votes are determined by its total number of representatives," Edelman says. "The same voters who are concerned about whether the electoral system is undemocratic are realizing that the method that determines the number of electoral votes their state gets is flawed."

While Edelman believes his method "gets the math right" as far as ensuring that the distribution of congressional representatives reflects the approach federal courts have taken in decisions in districting cases, he acknowledges that a fierce political battle would ensue if his approach were proposed.

"Inertia is also a powerful mathematical principle," he says.