Meet the Math Professor Who’s Fighting Gerrymandering With Geometry
Moon Duchin is an associate professor of math and director of the Science, Technology and Society program at Tufts. She realized last year that some of her research about metric geometry could be applied to gerrymandering — the practice of manipulating the shape of electoral districts to benefit a specific party, which is widely seen as a major contributor to government dysfunction.
.. 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.
.. So our first aim was to think like mathematicians about compactness and look at all the definitions that already exist, and compare them and try to prove theorems about the relationships between the definitions.
.. this landscape of compactness had a hole in it. It’s not that mathematicians hadn’t been working on it; it’s that [geometry experts] hadn’t entered the legal conversation.
.. the Polsby-Popper score; that’s the area of a district compared to the area of a circle of the same perimeter, given as a percentage.
.. 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.
.. 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?
.. Bouncing things off of diverse audiences has taught me things I didn’t already know about how rhetorically accessible different ideas are. This is well-known to educators: Once you achieve a certain level of expertise, it can be hard to find the difficult spots and the reasoning anymore because they’re so familiar to you.
.. the “efficiency gap.” It was a new metric of partisan gerrymandering that, for the first time, a court said they liked. The way it was devised was that the people who created it, they went back and they read all of Justice Anthony Kennedy’s written decisions about measuring gerrymandering. By reading his words and by reading what he said he found convincing and less convincing, they designed a statistic to appeal to him. He’s that vaunted median justice. If you can come up with something that will be convincing to Anthony Kennedy, then you’ve probably just changed the outcome.