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A blog written for those whose interests more or less match mine.

A Summer School for Mathematicians Fed Up with Gerrymandering

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Dawn Chan writes in the New Yorker:

On a late-spring evening in Boston, just as the sun was beginning to set, a group of mathematicians lingered over the remains of the dinner they had just shared. While some cleared plates from the table, others started transforming skewers and hunks of raw potato into wobbly geodesic forms. Justin Solomon, an assistant professor at M.I.T., lunged forward to keep his structure from collapsing. “That’s five years of Pixar right there,” he joked. (Solomon worked at the animation studio before moving to academia.) He and his collaborators were unwinding after a long day making preparations for a new program at Tufts University—a summer school at which mathematicians, along with data analysts, legal scholars, schoolteachers, and political scientists, will learn to use their expertise to combat gerrymandering.
The school, which began on Monday, is the brainchild of a young Tufts professor named Moon Duchin, who specializes in geometry. It has drawn participants from France, Israel, Japan, Singapore, and forty U.S. states. Some of Duchin’s students plan to train as expert witnesses, or to run for office. One mathematician enrolled out of a Christian sense of justice; another cited the day-to-day frustrations of living in a severely gerrymandered Florida district. Yet another applicant wrote, “Until very recently, I thought doing anything about this was a hopeless cause.” At the dinner, Duchin acknowledged that she was “kind of devastated by this election,” but both she and her colleagues were careful to point out that their venture is strictly nonpartisan. It was inspired by a simple question: What if there are well-researched areas of math that could simplify, or at least systematize, the fraught process of redistricting?
Gerrymandering has been a thorn in the side of the U.S. political system since before the very first Congress was elected. The Times editorial board recently called the issue “as old as it is corrosive to a representative democracy,” and last year, in a book titled “Ratf**ked,” the journalist David Daley wrote that “Democrats and Republicans alike have the sense that something in our politics is broken, that Congress is not responsive to the will of the people.” Although Americans of all political persuasions are able to agree on the problem, solutions, for now, are in short supply. In part, this is because even the most equitable districts are drawn according to subjective factors. A strangely shaped one might be a symptom of political bias, or it might merely reflect the local geography. Many states, moreover, explicitly call on their mapmakers to consider the needs of so-called communities of interest. As Michael Li, a senior counsel at the Brennan Center for Justice, told me, “There are districts that were drawn to keep communities in the foothills of the Santa Monica mountains together, because people said, ‘Gosh, our community of interest is we get wildfires. And we really care about having somebody represent us to make sure we get better fire protection.’ ” Conversely, someone could make the case that a district giving Democrats and Republicans proportional representation is unfair, because it precludes candidates who represent Spanish speakers, or millennials, or bird-watchers.
Perhaps for these reasons, the federal judiciary has often been wary about curtailing gerrymandering. One notable exception occurred in May, when the U.S. Supreme Court ruled that the North Carolina state legislature had unconstitutionally adjusted the boundaries of two congressional districts. The case revolved around a pair of familiar gerrymandering strategies, known as “packing” and “cracking.” When packing, you cram your adversary’s supporters into as few districts as possible, sacrificing one or two seats in order to keep control of many more; when cracking, you scatter those same supporters among districts that you will likely win anyway, effectively wasting their votes. In North Carolina, the Court found, the G.O.P.-led legislature had used a provision of the Voting Rights Act, which protects black voters from being cracked, essentially as an excuse to pack them. Since African-American voters, statistically speaking, tend to back Democratic candidates, the net result was fewer Democratic representatives.
But what happens when evidence of racial bias isn’t present, when the specific protections of the V.R.A. cannot be invoked? Some analysts have argued that a district’s lack of compactness or contiguity are good litmus tests for political bias. Another increasingly common approach, known as the efficiency gap, counts the number of votes wasted by each party in an election and looks at the disparity between them. The Supreme Court has yet to confirm which, if any, of these metrics can reliably stand up in court, but that could soon change. Two months from now, the Justices will hear arguments in Gill v. Whitford, the first case of partisan gerrymandering that they have considered in more than a decade. Anthony Kennedy, the Court’s swing vote, has in the past suggested that the right metrics—once they are shown to exist—could be used by judges to assess the fairness of new maps. As a result, Li told me, Gill will be “a big test.”
Although Duchin and her associates are debating existing metrics, they are also interested in developing new ones. Their impromptu potato-and-stick models, for instance, were meant to illustrate an idea that they have been exploring with growing enthusiasm. Conventional compactness tests, Duchin explained, focus on seemingly disparate geometric features. One type rewards shapes with a smooth perimeter, meaning that a district with the silhouette of, say, a circular-saw blade would flunk. Another type measures dispersion, or how far a district’s edges are from its center; a barbell-shaped district wouldn’t do so well here, while some saw blades might. Duchin believes that the two approaches can be reconciled using negative curvature, a property found in various surfaces—Pringles, saddles, the frilly parts of kale leaves. When you express the saw-blade-shaped and barbell-shaped districts as curved surfaces, rather than as flat ones, they turn out to have a good deal in common. “Political scientists had claimed that perimeters and dispersion were essentially independent of each other,” Duchin told me. “Negative curvature unites these scores.” The two districts—which previously passed and failed the same compactness tests, making for a murky debate—can now be subjected to the same holistic test.
Before dinner, Duchin’s group had invited Nestor Guillen, a Venezuelan mathematician teaching at the University of Massachusetts, Amherst, to give a talk on optimal-transport theory. Let’s say that you are the logistics officer of a fire department, and you need to divide your city into sections, each served by one of your stations.  . .

Continue reading.

Written by LeisureGuy

9 August 2017 at 3:13 pm

Posted in Election, Government, Law, Math

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