Easy to abuse, hard to prove

American lawmakers are often responsible for establishing voting districts within their respective states. Unfortunately, many have found ways to abuse this process to promote the election results they desire—a practice known as gerrymandering. Though there are a number of legal and practical requirements that lawmakers must adhere to when drawing districts, it remains possible to split a state into countless potentially legal district configurations with dramatically different electoral results. Given the number of options available, can we design a piece of computer software to find the best districting plan?

For Dr. Justin Solomon, that’s the wrong question to ask. “Basic human nature teaches us that we’ll never get everyone to agree on how to quantify what’s ‘fair.’ Even if we could, there are so many possibilities that multiple options would end up looking similar,” he says. “On top of that, automatic redistricting is not just difficult—it’s likely to be mathematically impossible in polynomial time. We need to approach the problem differently.”

Instead, together with collaborator Moon Duchin at Tufts and the Metric Geometry and Gerrymandering Group, he seeks to map out millions of example districts using computational methods to establish a baseline for what one might consider an “average” or “reasonable” redistricting proposal in a given context. Lawmakers could use this process as a check on redistricting by comparing their proposals with the larger landscape to determine if what they are suggesting is an outlier. For example, if Dr. Solomon’s team generates one million district plans and 99 percent of them share a common feature, lawmakers should look very closely at any proposal that goes against that trend.

Is this the time for change?

According to Dr. Solomon, funding for any work with a political flavor is hard to come by, as funding organizations are wary of becoming involved with America’s polarized political environment. “Our research is deliberately and fundamentally non-partisan,” he says. “Our goal is to promote fair redistricting practices.” The team’s efforts show the vast number of district plans that are possible, and how easy it is to game the system in a way that’s not immediately obvious. Unfortunately, the very nature of the current political climate makes it hard to find support for their work—which is why the Bose Grant opportunity stood out.

2020 vision—and beyond

Dr. Solomon hopes to develop models in advance of the redistricting that will follow the 2020 census. “In the short term, we hope to put together a computationally and mathematically well-founded approach to analyzing districting plans,” he says. This approach could help legislators evaluate their existing districts and any proposed changes arising from the census data. Ultimately, however, he aspires to much greater impact. “We’re working on establishing new mathematical theories that can be implemented in open-source software. And we’re performing outreach to help others understand the challenge and our solution by participating in conferences around the country,” he adds. “As a citizen, I firmly believe that voting is the foundation of our democracy. As researchers, we want to help create a stronger system that voters can believe in.”

Case-by-case

With the help of Dr. Solomon and as a result of increased political interest in the question of gerrymandering following the 2016 election, the Metric Geometry and Gerrymandering Group blossomed as a research enterprise over the duration of the Bose grant. As just one example, the team contributed analysis to the state legislature of Virginia in 2018 to assess various redistricting plans with respect to compliance with civil rights law. Furthermore, the team’s work was cited by Supreme Court Justice Elena Kagan in her dissenting opinion in Rucho v. Common Cause>. The Bose Fellows grant also helped to fund a full-time postdoctoral associate, Dr. Daryl DeFord, who served as a connector between Dr. Solomon’s lab at MIT and Dr. Duchin’s group at Tufts. Dr. DeFord is now in a tenure track position at Washington State University.

The team’s efforts succeeded in creating a widely-adopted tool for analyzing redistricting plans, but Dr. Solomon is realistic about the limitations of an algorithm when it comes to answering complex political questions. “While our algorithms have been used in legal cases, that’s not likely to be their primary function—especially as more and more courts rule that gerrymandering needs to be resolved at the legislative level rather than the judicial one,” he explains. “However, the broader question that our work tackled—how do you create something that is ‘representatively random’—is an ongoing line of inquiry for mathematicians. I’m excited by the work that we have done to apply theoretical methods like Markov Chain Monte Carlo to a real-world application with meaningful impact. We never could have explored these directions without the support of the Bose program.”