Tuesday, April 18, 2017

The mathematics of gerrymandering. (It's not as hard of a read as it sounds.)

The word “gerrymander” was coined in 1812 after Massachusetts governor Elbridge Gerry signed into law a salamander-shaped district.

Today, over two centuries later, “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.

But how do we measure gerrymandering? I suspect we share a common intuition that extreme imbalance in partisan makeup across districts is what we mean. But how do we measure “imbalance” and what is “extreme”?

2020 is just around the political corner so it is worth addressing these questions before we are forced to confront our ignorance.

Scientists - political, social, and computational - offer mathematical tools with which to measure gerrymandering and mathematically determine when partisan imbalance is intentional and egregious. Wired.com carries the research review in Gerrymandering is illegal, but only mathematics can prove it. (Above quotes and those that follow come from that report.)

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? …

… 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.

This is not merely an ivory tower exercise. There are real political and legal consequences of that research.

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.”

Expect more of the same as the research matures.

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.

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.

So what’s the problem motivating these mathematicians? For example, one criterion for judging whether a map is biased is the extent to which its districts are compact. If a district looks like a lizard wrapped around a tree, chances are that it was drawn with partisan motivation.

… In an assortment of racial gerrymandering cases, the Supreme Court has “stated repeatedly … that crazy-looking shapes are an indicator of bad intent,” …

… Chen and Rodden have used simulations … to suggest that Florida’s 2012 congressional plan was almost surely intentionally gerrymandered. Their expert testimony contributed to the Florida Supreme Court’s decision in 2015 to strike down eight of the plan’s 27 districts.

“We didn’t have this level of sophistication in simulation available a decade ago, which was the last major case on this topic before the [US Supreme] Court,” said Bernard Grofman, a political scientist at the University of California, Irvine.

The Florida ruling was based on the state constitution, so its implications for other states are limited. But the Wisconsin case has “potential incredible precedent value,” Grofman said.

Grofman has developed a five-pronged gerrymandering test that distills the key elements of the Wisconsin case. Three prongs are similar to those Stephanopoulos and McGhee have proposed: evidence of partisan bias, indications that the bias would likely endure for the whole decade, and the existence of at least one replacement plan that would remedy the existing plan’s bias. To these, Grofman adds two more requirements: simulations showing that the plan is an extreme outlier, suggesting that the gerrymander was intentional, and evidence that the people who made the map knew they were drawing a much more biased plan than necessary.

You can expect to see more such mathematically-grounded reasoning here at home when Arizona redraws its map in 2020.

I’ve left out a lot of examples of the measurements being studied so dive in to the wired.com article. It’s an easy read.

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