Hacking Cracking & Packing

The original gerrymander courtesy of Wikimedia Commons.

Sometimes the boundaries of voting districts can look really suspicious. If you’ve ever seen Illinois’ 4th Congressional District, you know what I mean. Sometimes there are good reasons for this; communities with common interests may want to vote together. But sometimes the reasons are bad; partisan politicians might be cracking and packing certain demographics. That is, cracking up certain demographic groups and scattering them through the districts and then packing all of the remainder into one often strangely shaped (perhaps dragon shaped?) district to minimize their votes. These are the classic tools of gerrymandering.

In the state of Wisconsin this practice has got particularly bad, and last week the supreme court heard oral arguments in the case of Gill v. Whitford. This case seeks to determine exactly how bad the partisan map rigging in Wisconsin is, and hopefully the outcome will be some sort of consensus on how to recognize and rectify the systematic disenfranchisement that comes with hardcore gerrymandering.

Jordan Ellenberg, a resident of Wisconsin, wrote about the case for The New York Times and explained why this might be of interest to us as mathematicians.

Over the summer, the Metric Geometry and Gerrymandering Group at Tufts University led by Moon Duchin, ran a summer camp where participants developed tools for detecting and understanding gerrymandering. As Duchin often points out, sometimes a weird looking district looks weird for a reason, so it’s important to find out why things look the way they do.

A few reasonable measures have been proposed. One being used in the Wisconsin case is called the Efficiency Gap, and it measures the net wasted votes as a share of the total votes in the state. Wasted votes are all votes cast for the losing candidate and all extra votes for the winning candidate, beyond what was needed to win. But as Olivia Watch illustrates in this graphic explainer for The Nib, efficiency gap can’t tell the whole story.

Another way to measure gerrymandering is to consider, in some systematic way, all possible redistricting schemes in a given state and compare them to what is being used. If the one being used is a significant outlier compared to the others, then it’s probably gerrymandered. A paper that recently appeared on the Arxiv uses this method to expose the badness of Wisconsin’s districting.

Recognizing and measuring gerrymandering is of course a totally different task from actually redrawing the lines in a fair and unbiased way. There are many schemes for this, but my favorite one to explain to strangers (and then watch them get all in a lather) is the shortest split line algorithm. It sort of disregards human interests, but hey, it makes really good looking maps!

This will not be the first time that math has been used to fairly distribute representation. Apparently Thomas Jefferson devised a sensible algorithm for assigning seats in congress by state. I imagine Jefferson might have something to contribute to our current discussion.

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