Yet it’s one thing to say bizarre-looking districts are suspect, and another thing to say precisely what bizarre-looking means. Many states require that districts should be reasonably “compact” wherever possible, but there’s no one mathematical measure of compactness that fully captures what these shapes should look like. Instead, there are a variety of measures; some focus on a shape’s perimeter, others on how close the shape’s area is to that of the smallest circle around it, and still others on things like the average distance between residents.
The Supreme Court justices have “thrown up their hands,” Duchin said. “They just don’t know how to decide what shapes are too bad.”
The compactness problem will be a primary focus of the Tufts workshop. The goal is not to come up with a single compactness measure, but to bring order to the jostling crowd of contenders. The existing literature on compactness by nonmathematicians is filled with elementary errors and oversights, Duchin said, such as comparing two measures statistically without realizing that they are essentially the same measure in disguise.
Mathematicians may be able to help, but to truly make a difference, they will have to go beyond the simple models they’ve used in past papers and consider the full complexity of real-world constraints, Duchin said. The workshop’s organizers “are absolutely, fundamentally motivated by being useful to this problem,” she said. Because of the flood of interest, plans are afoot for several satellite workshops, to be held across the country over the coming year.
Ultimately, the workshop organizers hope to develop a deep bench of mathematicians with expertise in gerrymandering, to “get persuasive, well-armed mathematicians into these court conversations,” Duchin said.