What Math Can Do for Your Country

Mathematics may be the solution to a complex and vexing public issue—gerrymandering.

By Jo Shroyer / Photography by Haley Nelson

Gerrymandering—the practice of drawing the boundaries of congressional and state voting districts to favor a particular party, political incumbent, or social group—has been called a fundamental threat to our democracy. It’s difficult to detect, however, and tough to prove. “Clearly a job for mathematics,” said Ellen Veomett, associate professor of mathematics at Saint Mary’s and winner of one of the 2019 Faculty Research Grants. Her research now focuses exclusively on developing and evaluating analytical tools that detect gerrymandering. She is not alone. Mathematicians have been quietly working on this problem for some time. “And now, there has been a huge explosion in proposed mathematical tools,” Veomett said.

The need is particularly urgent because of the looming 2020 census: States will be required to redraw their voting districts based on population changes. Since the last census in 2010, numerous lawsuits have challenged redistricting maps. Supreme Court Associate Justice Elena Kagan, in her opinion on Wisconsin’s Gill v. Whitford, described the 2010 redistricting cycle as producing “some of the worst partisan gerrymanders on record.” The court balked at engaging the case, however, in which a Republican legislature drew a new district map, along with a Maryland case, Benisek v. Lamone, regarding a map drawn by Democrats.

The court’s decision disappointed advocates calling for redistricting reform, but it also presented mathematicians with an opportunity to find ways to meet the court’s demands, Veomett said. The justices asked for a clear, accurate, and objective standard for detecting and proving gerrymandering. Veomett and her colleagues in the Metric Geometry and Gerrymandering Group (MGGG) were paying attention.

MGGG, based in Boston, is a team of mathematicians, legal scholars, and geographic information systems analysts committed to studying the use of computing and geometry in U.S. redistricting. They offer training for mathematicians, teachers, legal scholars, and others to increase awareness and understanding of what can be a frustratingly arcane topic.

In her work with the MGGG, Veomett has noticed that people from different disciplines view gerrymandering through their own particular lens, perhaps introducing human bias. That’s why it’s important to involve people with a wide range of expertise, including mathematicians. “We are experts in finding the unusual case or the single contradiction. We can look at specific metrics, push them to their extreme, and figure out what appears to be fair and what doesn’t.

“But I think that while mathematicians may disagree about which metric to use, we will focus on the mathematics of the problem rather than cherry-pick a metric that’s going to say what we want.”

Veomett has studied two metrics intended to detect gerrymandering: the Efficiency Gap and the Declination. The Efficiency Gap is based on the idea of “wasted votes.” A vote is called wasted if it does not contribute to a candidate’s election. Thus, any vote for a losing candidate as well as any vote beyond the 50 percent needed for a candidate to win is considered wasted. Use of this metric played a key role in the Gill v. Whitford arguments.

“The Efficiency Gap’s creators wanted to create a metric that has higher values on elections where party A wins more seats and lower value on elections where party A wins fewer seats,” said Veomett. Her research published in The Election Law Journal, however, proved otherwise, “due to the unexpected effect of uneven voter turnout,” she added. The Declination metric compares the number of seats won by a specific political party, the average vote share for that party in districts it won, and vote share in districts that it lost. “The idea is that gerrymandering happens when some of party A’s voters are packed into districts that it wins with an overwhelming majority, and the rest of party A’s voters are cracked among the remaining districts, which it loses.

Declination tries to detect this packing and cracking.” A forthcoming publication by Veomett, Saint Mary’s student Andrea Padilla ’19, and mathematicians Marion Campisi and Thomas Ratliff shows that the Declination detects gerrymandering in competitive states but has a hard time detecting bias in highly partisan states. Veomett and her collaborators are also designing their own gerrymandering detection tool. “All of the previously designed metrics are calculated from either election data or the districting map. But it’s not hard to see that both matter; if a mapmaker wants to gerrymander, he or she needs to know both voter preferences and where voters with each preference are living in the state.” Veomett’s team’s metric incorporates both voter preferences and the districting map to more accurately detect gerrymandering.


"While Mathematicians may disagree about which metric to use, we will focus on the mathematics of the problem rather than cherry-pick a metric that’s going to say what we want…we go for the facts.” — Ellen Veomett

Veomett has also reached out to policy makers and the general public about this civic concern. Last June, she coauthored an op-ed in political news outlet The Hill with her husband, Aaron Rappaport, a professor of law at UC Hastings and former assistant director of the White House National Economic Council. In their article, the duo described the benefits and shortcomings of mathematical solutions to gerrymandering. “I think most mathematicians believe that the most reasonable and most promising tool is outlier analysis, which really encompasses a lot of different tools,” Veomett said.

Veomett’s and Rappaport’s opinion piece also pointed out a silver lining in last year’s Supreme Court gerrymandering decision. “The petitioners were simply not ready to fully answer the questions that swing justices, particularly Associate Justice Anthony Kennedy, want answered,” they wrote. Justice Kennedy left the door open for future rulings, offering guidance on how plaintiffs could establish standing to bring suit—a claim of personal injury to individual voting districts as a result of redistricting.

The court, which now includes Associate Justice Brett Kavanaugh, who took the place of the retired Justice Kennedy, is currently reconsidering the constitutionality of political gerrymandering by reviewing two lower court cases—one in Maryland, regarding a district map drawn by Democrats, and another in North Carolina, with a district map drawn by Republicans. Its review includes consideration of many of the mathematical metrics Veomett researches, including the Efficiency Gap and others.

Veomett strongly believes in math’s power to tame gerrymandering. “Mathematics is nonpartisan; these metrics are like fancy thermometers, and mathematics can describe exactly what those thermometers read. I do believe that math is pure. Mathematicians go for the facts.”

The high court’s decision is expected by June 2019.