Can Math Detect Gerrymandering?

  • By Ari Daniel
  • Posted 10.05.17
  • NOVA

The Supreme Court is hearing a case about gerrymandering in Wisconsin, and mathematicians are watching closely. Here's why.

Running Time: 03:05


Onscreen: Gerrymandering is when Congressional districts are drawn to favor one party or candidate over another. The word comes from Elbridge Gerry. In 1812, Governor Gerry helped create a Massachusetts district resembling a dragon or a salamander.

Moon Duchin: Gerrymandering is generally a blanket term for abuses in redistricting. With the pen, comes the power.

Onscreen: Can math help detect gerrymandering? According to the Constitution, each Congressional district should have roughly the same population.

Kristen Clarke: The census bureau releases data at the start of a decade showing how populations shift. That data is then used by lawmakers to redraw districting maps.

Onscreen: It's legal for politicians to do a little finessing of boundaries to help their own party. And it's up to the courts to determine when lines run afoul of the Constitution. Here are a couple ways to gerrymander. Let's say this is a state. Each block is a voter voting for one of two parties. It's a 50-50 split. Draw districts like this, and the voters are split equally.

Duchin: Packing is where you stuff too many of your opponents' voters into too few districts so that they get fewer seats out. Cracking is where you take your opponents' voters and you disperse them over several districts rather than letting them be sufficiently concentrated into one.

Onscreen: Both packing and cracking distribute an opponent's votes so they're less effective. These are known as “wasted votes.”

This week the Supreme Court hears the case Gill v. Whitford. The plaintiffs argue in part that Wisconsin's 2012 State Assembly districts were drawn so one party would “waste” many more votes than the other party. And that THIS was a sign of gerrymandering. In other court cases, plaintiffs have claimed that some shapes point to gerrymandering. But there are no clear rules for shaping districts.

Duchin: Who out there is equipped maybe to tell us when a shape is a good shape and when a shape is a bad shape? Well, there's this whole field called geometry where that's kind of what we do is we think about shape.

Onscreen: So can shape analysis identify gerrymandering? Mathematician Moon Duchin thinks a clue may lie in curvature.

Duchin: Curvature literally means how bendy something is.

Onscreen: The team creates a network of lines based on population density. Then folds along the lines like origami. This folding approach can reveal weak spots in the district’s geometry that Duchin thinks could signal gerrymandering. She's developing formulas to help lawmakers draw districts that are geometrically and constitutionally sound. So that one day, geometry might help stop gerrymandering.

Clarke: It's exciting to have mathematicians be a part of the dialogue. By bringing their expertise to bear, I think we position ourselves to end up with maps that provide all communities an equal opportunity to elect candidates of their choice.



Ari Daniel
Production & Research Assistance
Ivy Liu, Theresa Machemer, and Elena Renken
Editorial Review
Julia Cort & Tim De Chant
© WGBH Educational Foundation 2017


Assaf Bar-Natan
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(main image: Original gerrymandering political cartoon)

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