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How to Quantify (and Fight) Gerrymandering

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Gerrymandering is under strong attack on several fronts, and we may see the end of it by 2020 (when the next big redistricting will occur following the 2020 census). Erica Klarreich writes in Quanta:

Partisan gerrymandering — the practice of drawing voting districts to give one political party an unfair edge — is one of the few political issues that voters of all stripes find common cause in condemning. Voters should choose their elected officials, the thinking goes, rather than elected officials choosing their voters. The Supreme Court agrees, at least in theory: In 1986 it ruled that partisan gerrymandering, if extreme enough, is unconstitutional.

Yet in that same ruling, the court declined to strike down two Indiana maps under consideration, even though both “used every trick in the book,” according to a paper in the University of Chicago Law Review. And in the decades since then, the court has failed to throw out a single map as an unconstitutional partisan gerrymander.

“If you’re never going to declare a partisan gerrymander, what is it that’s unconstitutional?” said Wendy K. Tam Cho, a political scientist and statistician at the University of Illinois, Urbana-Champaign.

The problem is that there is no such thing as a perfect map — every map will have some partisan effect. So how much is too much? In 2004, in a ruling that rejected nearly every available test for partisan gerrymandering, the Supreme Court called this an “unanswerable question.” Meanwhile, as the court wrestles with this issue, maps are growing increasingly biased, many experts say.

Even so, the current moment is perhaps the most auspicious one in decades for reining in partisan gerrymandering. New quantitative approaches — measures of how biased a map is, and algorithms that can create millions of alternative maps — could help set a concrete standard for how much gerrymandering is too much.

Last November, some of these new approaches helped convince a United States district court to invalidate the Wisconsin state assembly district map— the first time in more than 30 years that any federal court has struck down a map for being unconstitutionally partisan. That case is now bound for the Supreme Court.

“Will the Supreme Court say, ‘Here is a fairness standard that we’re willing to stand by?’” Cho said. “If it does, that’s a big statement by the court.”

So far, political and social scientists and lawyers have been leading the charge to bring quantitative measures of gerrymandering into the legal realm. But mathematicians may soon enter the fray. A workshop being held this summer at Tufts University on the “Geometry of Redistricting” will, among other things, train mathematicians to serve as expert witnesses in gerrymandering cases. The workshop has drawn more than 1,000 applicants.

“We have just been floored at the response that we’ve gotten,” said Moon Duchin, a mathematician at Tufts who is one of the workshop’s organizers.

Quantifying Bizarreness

Gerrymanderers rig maps by “packing” and “cracking” their opponents. In packing, you cram many of the opposing party’s supporters into a handful of districts, where they’ll win by a much larger margin than they need. In cracking, you spread your opponent’s remaining supporters across many districts, where they won’t muster enough votes to win.

For instance, suppose you’re drawing a 10-district map for a state with 1,000 residents, who are divided evenly between Party A and Party B. You could create one district that Party A will win, 95 to 5, and nine districts that it will lose, 45 to 55. Even though the parties have equal support, Party B will win 90 percent of the seats.

Such gerrymanders are sometimes easy to spot: To pick up the right combination of voters, cartographers may design districts that meander bizarrely. This was the case with the “salamander”-shaped district signed into law in 1812 by Massachusetts governor Elbridge Gerry — the incident that gave the practice its name. In an assortment of racial gerrymandering cases, the Supreme Court has “stated repeatedly … that crazy-looking shapes are an indicator of bad intent,” Duchin said.

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.

The Accidental Gerrymander

A compactness rule would limit the range of tactics available for drawing unfair maps, but it would be far from a panacea. For starters, there are a lot of legitimate reasons why some districts are not compact: In many states, district maps are supposed to try to preserve natural boundaries such as rivers and county lines as well as “communities of interest,” and they must also comply with the Voting Rights Act’s protections for racial minorities. These requirements can lead to strange-looking districts — and can give cartographers latitude to gerrymander under the cover of satisfying these other constraints. . .

Continue reading.

Written by LeisureGuy

4 April 2017 at 3:27 pm

Posted in Math, Politics

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