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Student Team Addresses Gerrymandering With Mathematics

Project develops nonpartisan way to assess the fairness of congressional districts

Students on the Data+ team are looking to quantify the effect of gerrymandering on congressional elections.
Students on the Data+ team are looking to quantify the effect of gerrymandering on congressional elections.

A Duke University research team has applied mathematical modeling techniques to develop a novel, nonpartisan way to assess the fairness of congressional districts.

The team led by mathematics professor Jonathan Mattingly found that states with independent redistricting commissions, such as Iowa, had statistically fairer results than states with partisan redistricting systems, such as North Carolina and Maryland.

They also evaluated the districts drawn earlier this fall by a mock bipartisan redistricting panel formed by Terry Sanford Distinguished Fellow Tom Ross. The “Beyond Gerrymandering” project panelists were former North Carolina Supreme Court justices and lower court judges.

In partisan systems, the party that controls the state legislature typically draws boundaries to favor its own candidates, a practice known as gerrymandering. Politically gerrymandered districts have contributed to a congressional climate in which only small a fraction of U.S. Representatives face serious opposition in most elections.

“When random districts are drawn and the results of previous elections are re-tabulated,” said Mattingly, “the results shed light on the ways gerrymandered political boundaries stifle disparate political voices. The same voters, arranged into different districts, would have produced vastly different results.”

In North Carolina, the research team examined the state’s 2012 congressional elections, in which Democrats won a majority of the popular vote but won just four of North Carolina’s 13 congressional districts.

“In our samples, Democrats win five, six and even seven congressional districts with far greater frequency than four, confirming that the observed outcome is indeed very odd,” the research team wrote.

Initially, Mattingly worked with a team of undergraduate and graduate students during the summer of 2015 to analyze the congressional redistricting efforts in North Carolina, Tennessee, Maryland, New York, Texas, Iowa, Wisconsin and Arizona.

Their process and results are available on a website, Quantifying Gerrymandering.

More recently, a second team developed two indices to characterize a state’s congressional districts: An index of gerrymandering and an index of representativeness. The first measures how packed the districts are. Packing is the act of concentrating one party in a few districts to minimize the effect of their votes statewide, and tends to create more partisan districts. The second index measures how representative the results are for a given set of districts over a series of elections.

Using these ideas, Mattingly’s team analyzed maps produced by Ross’s “Beyond Gerrymandering” project.

They compared the outcomes using the mock panel’s map and those used in the 2012 and 2016 N.C. congressional elections to the hypothetical outcomes of thousands of alternative district maps. They found that those produced by the mock panel of judges scored much better on the indices of gerrymandering and representativeness.

The alternative maps were drawn using the same criteria that guided the creation of the actual maps: Equal populations in each district, compactness, number of counties that are split into multiple districts, and the share of the minority voting age population within the districts.

Mattingly said the project was intended as a nonpartisan demonstration.

“Our purpose is not to create a panacea for political map drawing. Rather, we wanted to provide a nonpartisan, objective way of determining which sets of districts are more representative and less gerrymandered,” he said.

Students involved in the project in the summer of 2015 were Sachet Bangia, Bridget Dou and Sophie Guo, undergraduates at Duke, and Christy Vaughn Graves, now a graduate student at Princeton.

The 2016 team consisted of visiting assistant professor Gregory Herschlag, graduate student Robert Ravier and undergraduates Justin Luo and Hansung Kang.