Can Geometry Root Out Gerrymandering?

IRA FLATOW: Republican legislators in Wisconsin have been ordered to redraw the latest map of state legislature districts after federal judges found the districts unconstitutional, gerrymandered to favor Republican candidates. Since the state is appealing that decision, this case could go to the Supreme Court this year. And the Wisconsin case is one of many battles over allegedly partisan district lines taking place around the country right now. There are others unfolding in Texas, North Carolina and elsewhere.

What does a gerrymandered district look like? Well, here’s one hint, if the district looks more like a salamander, or some other Rorschach ink blot, it might have been drawn to favor one party over another. If it’s more round, chances are it’s fair. And my next guest wants to train mathematicians to bring mathematical logic to the shape of fairness, train them as expert witnesses in court cases, where judges must rule on the fairness of a district.

Moon Duchin, Associate Professor of Mathematics, and Director of the Science, Technology and Society Program at Tufts University in Medford, Massachusetts is working on that. Welcome to Science Friday.

MOON DUCHIN: Thank you. Hi.

IRA FLATOW: How do we train mathematicians and why do we need mathematicians to be expert witnesses for gerrymandering cases?

MOON DUCHIN: Well, I’d say that the standard of compactness for congressional districts is really elusive and courts have said so repeatedly. We’ve had some justices saying that we know a bizarre, irrational shape when we see it, but we don’t know what precisely should the threshold be, which makes a shape too tortured, or irregular, or unreasonable. And the mathematicians, geometers like me, we study this and we think we might have something to say that’s helpful in making an intervention into deciding when a shape looks a little bit too strange to be fair.

IRA FLATOW: You talked about this idea called compactness, is that how you measure the gerrymandering whether it’s fair or not?

MOON DUCHIN: Well the word compactness appears a lot. It appears in many state constitutions, it’s not in the US Constitution, but it’s become a traditional distracting principle. So courts look to see that a shape is compact, well they would, but the problem is nobody knows what it means. So there are competing– there’s just dozens of competing possible definitions of compactness and that cacophony of definitions has been one of the problems. So one of the things I think mathematicians can contribute is a sense of what the definitions have in common at a deeper level, some sort of deeper structure that shows you what makes a shape seem weird to the eye.

IRA FLATOW: Give us a little more– we like to talk math and Science Friday, give us a little idea little more in-depth of how you measure the compactness mathematically.

MOON DUCHIN: Well, absolutely. So one of the popular ideas, which I think is the first thing that your standard geometer would propose if you were to ask the question in the street is an iso-parametric ratio. So that looks at the area compared to the perimeter. And if you want to make a good score out of that you should really compare that area to the perimeter squared, so that you get something that’s invariant under scale. Because after all we’re looking for something that measures a shape and not its size. A bigger and a smaller shape should come out about the same or exactly the same.

So area to perimeter squared is a really classic score and we’ve known for a very long time, thousands of years actually, that circles are optimal for this kind of iso-parametric ratio. That wasn’t actually proved till the late 19th century, but it was written about long ago Virgil’s Aeneid. So that’s one thing you might do, but there are many others. In particular, you might think that a score that favors circles might not be the best, because circles don’t pack together to make nice congressional districts in a state.

So another thing you could do and something that my group is really thinking about is dispersion. You could look at average distance. You could ask the voters in the state, how far apart are they from each other. Or how long would they have to travel to get to a town hall and yell at their congressmen in person. I like to think that one’s pretty accessible.

IRA FLATOW: Let me remind everybody that this is Science Friday from PRI, Public Radio International. Talking with Moon Duchin about compactness of gerrymandering districts. Are judges looking for a measurement? Would they– do they welcome an independent the mathematicians might independently come in and help them rule on the district?

MOON DUCHIN: Well, I found that mathematicians haven’t made their way into the courtroom very often. So we’ve seen a lot of statistical arguments advanced with various degrees of success, but we’re not seeing a whole lot of geometry in the courtroom. And I think that one reason is that if you look at the history, you’ll see some skepticism, you’ll see the courts asking for just one measure. If there are all these different ones and they’re all a little bit different, the court feels that there’s a sink it there.

So one thing I’d like to try to train mathematicians in how to talk about is that these days there’s been a breakthrough recently in our ability to take many scores into account at once. And it’s actually– computers have been a double edged sword for redistricting. On one hand they give you the ability to make more and more precise gerrymanders. But on the other hand now recently for the first time they give you the ability to detect gerrymanders.

So these days there are powerful supercomputer algorithms that can take multiple compactness scores into account. And do what I like to call mind reading with supercomputers. That they can look around in the space of alternative maps and figure out is a map that’s in place, like say the current maps in North Carolina, Wisconsin, is it an outlier among comparably good maps that all have compactness scores that are as good, equal population, preserved communities of interest, and all the other traditional districting principles. If the current map really stands out among 10,000 alternatives, that’s probably a red flag.

IRA FLATOW: Now, you’re training mathematicians to become good expert witnesses, how do you know that the mathematicians who take these workshops will actually be called as expert witnesses?

MOON DUCHIN: Yeah, that’s a great question. So one thing that we’re doing is we’re working together across disciplinary lines. So it’s not just mathematicians, but we have political scientists, law scholars, and litigators that are involved. So we’ve been working closely in particular with a wonderful nonprofit based in D.C. called the Lawyers’ Committee for Civil Rights Under Law and they actually file a lot of these voting rights cases. And so by partnering with litigators who know what we’re about and who can help us think about useful training we think we’ll be able to provide a big bench of new people to diversify the expert witness pool and to be available to be on hand in this landscape right now with so many voting rights cases coming forward.

IRA FLATOW: If some mathematics folks want to get involved, how do they get involved with you or get the training?

MOON DUCHIN: Right, great question. So we’re actually running– in August we’re running a training at Tufts, at my home institution. But then we have regional trainings that will be running in some of the various states we’ve been talking about. We’re going to Wisconsin and then North Carolina. We’re going to Texas and California. And if folks want to find out more about what we’re doing, we have a website, it’s sites.tufts.edu slash gerrymander with no final e, g-e-r-r-ym-a-n-d-r, gerrymandr. And you can probably find it by Googling.

But, yeah, we’re called the Geometry of Redistricting Summer School. My working group is called the Metric Geometry and Gerrymandering Group. And we will be working for the next few years, getting ready for the 2020 census, to get the word out and get lots of people trained and try to really mobilize the math community to speak up and have a voice in redistricting.

IRA FLATOW: Well, as this gets going we’ll have you back on. OK, Moon?

MOON DUCHIN: Terrific.

IRA FLATOW: Moon Duchin, Associate Professor of Math at Tufts University in Medford.

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