Will Geometric Group Theory Be the Solution to the United States' Gerrymandering Problem?

A new initiative lead by a Tufts University mathematics professor thinks this field of research could be the best shot at designing fair congressional districts apolitically.

Published Feb 25, 2017

 (Wikimedia Commons)
Image Via Wikimedia Commons

On 22 February 2017, The Chronicle of Higher Education published an interview with Tufts University math professor Moon Duchin, who recently announced an initiative to train a "new generation of expert witnesses" about the mathematical principles that could be used to limit the congressional redistricting strategy known as gerrymandering in as fair a manner as possible.

Gerrymandering is the practice of strategically drawing congressional districts — something constitutionally required to occur every ten years — to limit the influence of some votes and/or elevate the influence of others. A 2010 white paper by geospatial firm Azavea describes the process:

There are two primary strategies employed in a gerrymander: “packing” and “cracking”. Packing refers to the process of placing as many voters of one type into a single district in order by reduce their effect in other, adjacent districts. If one party can put a large amount of the opposition into a single district, they sacrifice that district, but make their supporters stronger in the nearby districts. The second technique, cracking, spreads the opposition amongst several districts in order to limit its effect.

Congressional redistricting, though putatively a local issue, can have (and has had) a major effect on national politics, most recently in the redistricting that followed the 2010 census. During this time, the national GOP poured money into local state elections to gain control of the individual legislative bodies in charge of drawing the new maps. David Daley, editor-in-chief of and author of Ratf*cked: The True Story Behind The Secret Plan To Steal America's Democracy, described that effort in a 15 June 2016 interview on NPR’s Fresh Air:

The idea was that you could take a state like Ohio, for example. In 2008, the Democrats held a majority in the state house of 53-46. What RedMap [a GOP initiative behind the redistricting strategy] does is they identify and target six specific statehouse seats. They spend $1 million on these races, which is an unheard of amount of money coming into a state house race. Republicans win five of these. They take control of the state house in Ohio - also, the state Senate that year. And it gives them, essentially, a veto-proof run of the entire re-districting in the state.

So in 2012, when Barack Obama wins again and he wins Ohio again, and Sherrod Brown is re-elected to the Senate by 325,000 votes, the Democrats get more votes in statehouse races than the Republicans. But the lines were drawn so perfectly that the Republicans held a 60-39 supermajority in the House of Representatives, despite having fewer votes. [...]

There are two prongs of this effort. The first prong, of course, is winning these races in 2010. Then in 2011, you have to be ready to redraw the maps. And what the Republicans were able to do in states like Ohio and Pennsylvania and North Carolina, and Michigan and Florida and Wisconsin was move the redistricting process deep behind closed doors and use redistricting as a blunt force partisan weapon in a way that it had not been all the way back to the first gerrymander in 1790.

While there are rules that aim to limit the abuse of this practice, they leave a problematic amount of space for interpretation. Speaking to The Chronicle, Duchin explained the goals of her initiative, named the Metric Geometry and Gerrymandering Group (MGGG), and explained why the field could benefit from mathematicians:

In redistricting, one of the principles that’s taken seriously by courts is that districts should be compact. The U.S. Constitution does not say that, but many state constitutions do, and it’s taken as a kind of general principle of how districts ought to look.

But nobody knows exactly what compactness means. People just have the idea that it means the shape shouldn’t be too weird, shouldn’t be too eccentric; it should be a kind of reasonable shape. Lots of people have taken a swing at that over the years. Which definition you choose actually has stakes. It changes what maps are acceptable and what maps aren’t. If you look at the Supreme Court history, what you’ll see is that a lot of times, especially in the ’90s, the court would say, Look, some shapes are obviously too bizarre but we don’t know how to describe the cutoff. How bizarre is too bizarre? We don’t know; that sounds hard. [...]

What courts have been looking for is one definition of compactness that they can understand, that we can compute, and that they can use as a kind of go-to standard. I don’t have any illusions that we’re going to settle that debate forever, but I think we can make a contribution to the debate.

In an effort to achieve this goal, Duchin has announced a five-day-long meeting and training program planned for the summer of 2017, as described by the Chronicle:

Because of the increase in cases challenging new electoral maps, she says, there’s a need for expert witnesses who understand the mathematical concepts applicable to gerrymandering.

To meet that need, she’s spearheaded the creation of a five-day summer program at Tufts that aims to train mathematicians to do just that. The first three days of the program will be open to the public and available online, with lessons that put redistricting in legal, historical, civil-rights, and mathematical contexts. Attendees of the program’s final two days will participate in one of three specialized tracks on giving expert testimony, teaching, and working with geographic-information systems.

In terms of her own background relevance, she said that — serendipitously — her academic expertise was well suited to this question:

In geometric group theory, I work on what’s called metric geometry and within that, I already had a series of papers that were about essentially the average distances between points in various kinds of shapes. That’s actually directly applicable to compactness. It turns out that if you take a district and you look at the average distances between all of its points, then the bigger that is, the less compact, once you normalize by the diameter. That meant that I already had published theorems that, I think, cast some light on the districting problem.

Other researchers have tackled this issue in the past, Duchin said, but she added that part of the goal for this summer program is to bring a number of people together to share their ideas and expertise as well:

The point of the summer school isn’t just to bring people together so we can convince them of our ideas. We also want to pool ideas and see, putting all those brilliant people in one place, can we make some progress on what’s been a pretty intractable problem?

On Fresh Air, Daley agreed that the problem has no easy solution, and that taking redistricting out of legislators hands likely won’t be happening anytime soon. “I do not think that this is a problem that can be solved quickly or easily,” he said.


Najmabadi, Shannon.   "Meet the Math Professor Who’s Fighting Gerrymandering With Geometry."     The Chronicle of Higher Education.   22 February 2017.

Azeva White Paper.   "Redrawing the Map on Redistricting 2010: A National Survey."     2009.

Daley, David.   Ratf**ked: The True Story Behind the Secret Plan to Steal America's Democracy..     W. W. Norton & Company, 2016.   9781631491634   "Understanding Congressional Gerrymandering: 'It's Moneyball Applied To Politics."     15 June 2016.   "Redistricting Criteria."     1 January 2016.

Polsby, Daniel, D., and Popper, Robert, D.   "The Third Criterion: Compactness as a Procedural Safeguard Against Partisan Gerrymandering."     Yale Law & Policy Review.   1991.

Alex Kasprak is an investigative journalist and science writer reporting on scientific misinformation, online fraud, and financial crime.

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