Could Math Solve the Gerrymandering Problem?

By Lakshmi Chandrasekaran

Ever since the Supreme Court heard two gerrymandering cases—from Indiana in 1986 and Pennsylvania in 2004—it has recognized partisan gerrymandering as a problem. However, the justices have been unable to agree on a manageable standard to evaluate gerrymandering claims. 

Bridging the Gap?

To satisfy this concern, Nicholas Stephanopoulos, a professor at the University of Chicago Law School, devised a metric known as “efficiency gap”. Stephanopoulos, who is also a lawyer representing the plaintiffs in Wisconsin’s Gill v. Whitford gerrymandering case, worked with Eric McGhee, a political scientist at the Public Policy Institute of California to create the quantitative measure. Efficiency gap is a mathematical formula that takes into account the number of “wasted votes” from each party in an election, to determine if the party could convert the number of votes cast for it in any given state into proportional seat wins. Votes for the losing candidate and excess votes for the winning candidate (more votes scored by the candidate than required to win) are classified as “wasted votes”. Taken together, the ratio of wasted votes to that of total number of votes cast yields a value known as “efficiency gap”. As an equation, here’s how the efficiency gap (EG) would look:

EG = (Total Democratic wasted votes- Total Republican wasted votes)/(Total Votes)           (1)

In an ideal scenario, the wasted vote is zero so there would be no efficiency gap - in other words, no partisan redrawing of legislative boundaries. “Hopefully, the record we've developed in the Wisconsin case, combined with our advocacy, will convince the Court that the efficiency gap (or other measures!) can be used to quantify gerrymandering,” said Stephanopoulos.

However, in last fall’s hearing of Gill v. Whitford, the Supreme Court justices seemed equally divided about assessing the merits of the efficiency gap measure as a tool to quantify political gerrymandering. Justice Kennedy, the swing vote on the bench quizzed the appellants (representing Wisconsin) extensively on political matters pertaining to the constitutionality of partisan gerrymandering, while remaining silent during the arguments presented by the opposing side. With the Wisconsin’s solicitor general positing that the efficiency gap measure was just an estimate and not a scientific method, Justice Sotomayer argued “They’re estimates - you haven’t put any social scientist (on the stand) to say that the estimates are wrong. You have poked holes, but every single social science metric points in the same direction,” highlighting how the metrics expose maps drawn to partisan advantage. However, the conservative Chief Justice Roberts was dismissive of the efficiency gap measure and called it “sociological gobbledygook”, which earned him a spirited rebuttal from the American Sociological Association. Conservative Justice Alito brought up a relevant point, “Has there been a great body of scholarship that has tested this efficiency gap?” – thus questioning the scientific rigor of the newly minted method. Overall, the comments expose the dichotomy of the bench and their hesitation in relying on a mathematical metric to address whether the makeup of a state legislature adequately represents the will of the voters.

More the Merrier

However, this is by no means the only method to quantify gerrymandering. It turns out that gerrymandering recently caught the math bug. Nationwide, numerous scientists have come up with different quantitative measures and mathematical models to measure gerrymandering.

Jonathan Mattingly, a professor of mathematics at Duke University, has been investigating gerrymandering practices using Markov Chain Monte Carlo models on a sampling of maps, as part of the Data+Program and Information Initiative at Duke. One of the key takeaways from Mattingly’s simulations is that Democratic losses in the 2012 and 2016 North Carolina congressional elections can be attributed to partisan gerrymandering.

Utilizing big data and advanced computing techniques, Wendy Cho, political science professor at the University of Illinois-Urbana Champaign, has devised a computer algorithm that asks whether the structure of any given district can occur by chance. Cho runs and re-runs her algorithm by slightly tweaking certain parameters each time—say, by maintaining a slightly unequal population across districts—and producing a new map. Cho calls them “reasonably imperfect” maps. Her algorithm creates billions of maps, which are then compared to the original district map. If the original map is not generated by this machine-spewed set of maps, then that, she says, is evidence of gerrymandering.

Now, could a district have biased boundaries based on its shape? This has stoked the interest of Professor Moon Duchin at Tufts University who founded The Metric Geometry and Gerrymandering Group (MGGG) to help lead geometry-based efforts to tackle gerrymandering.

Last August, a group of metric geometers and social scientists came together for The Geometry of Redistricting workshop at Tufts University, organized by MGGG. The event encompassed math, law, and civil rights. Justin Solomon, engineering professor at the Massachussets Institute of Technology and part of the MGGG team, applies geometric principles to investigate gerrymandering. Speaking at the conference, Solomon talked about finding the “right hill to climb” – thus describing the challenges of choosing the right parameter, such as graph curvature, equal population, minority representation etc., to optimize first and explore the politicial redistricting problem using computational methods. “Since there are 435 congressional districts, each of different sizes and shapes, that makes it harder to develop an accurate software for redistricting,” Solomon said, highlighting the magnitude of the problem.

Left or Right?

“With respect to partisan gerrymandering, it's currently Democrats who are disadvantaged at the congressional and state legislative level. This hasn't always been the case; in the 1970s and 1980s, for example, it was Republicans who were handicapped,” says Stephanopolous.

However, Robert Bennett, Professor of Law Emeritus at Northwestern University said gerrymandering affects everyone who votes. The real issue in gerrymandering is the problem of typecasting the voter. In most gerrymandered districts there is hardly any competition between Democrats and Republicans since the district is designed to produce a known outcome. The losing party does not field a candidate in such districts, diverting money into more competitive districts. This creates little motivation for candidates to reach out to voters. “That is most clearly true for those confident of winning and who have no incentive to speak to the district’s minority, but also to the district’s majority, except in very rote ways. The real effects of gerrymandering are thus on the candidates (and of course on the resulting complexion of the governing body as a whole), who don’t really have to compete for votes,” says Bennett.

Whether gerrymandering manifests on a local or national level, the problem remains the same - it results in a complete disconnect between elected leaders and the people. As Bennett says, “The immediate effects of gerrymandering are on the campaigning that the electorate hears. The district minority will hear little at all, and the majority will hear little genuine engagement with real issues of public policy.”

Lakshmi Chandrasekaran received her Ph.D. in mathematical sciences from the New Jersey Institute of Technology. She is currently pursuing her masters in science journalism at Northwestern University, and is a freelance science writer whose work has appeared in several outlets. She can be reached on Twitter at @science_eye.