Countering a Political Problem with 'Beautiful' Math
by Kevin Donahue
“Beautiful” isn’t a word used in politics much lately.
But that’s how Kristopher Tapp, Ph.D., sees mathematics’ role in addressing one of the most impactful issues in the electoral landscape — gerrymandering, the partisan manipulation of voting district boundaries meant to benefit one political party.
The debate over gerrymandering, which has been going for at least 200 years, has seen renewed fervor and even resulted in the redrawing of Pennsylvania’s voting districts ahead of the 2018 midterm elections.
Tapp, the chair of mathematics at SJU, has completed a research paper titled “Measuring Political Gerrymandering,” which he submitted for an upcoming issue of American Mathematical Monthly. In it, he evaluates one method of quantifying gerrymandering, the efficiency gap, and suggests improvements to the model.
Tapp became interested in the use of mathematics to identify and address gerrymandering about a year ago. He has since written his paper and spoken at several conferences on the subject.
“It sucked me in because it included a little geometry, which is along the lines of research problems I’ve studied before,” he says, “and I saw that it was relevant to a really important court case going on in Wisconsin.”
The case, Gill vs. Whitford, filed in 2016, resulted in a Wisconsin court striking down the state assembly map. The decision was appealed to the U.S. Supreme Court, which sent it back to a lower court. It is expected to return to the Supreme Court in 2019.
The Wisconsin verdict pivoted on the efficiency gap, a formula that considers votes for the losing candidate, and those on the winning side far in excess of the number needed to win the election, to be “wasted.”
“It’s a newish formula, invented in 2014,” Tapp says. “It’s very simple, a beautiful formula that looks at an election outcome and measures the extent to which it satisfies a reasonable fairness principle; namely that the two parties should ‘waste’ about the same number of votes.”
This is important because gerrymandering is a partisan attempt to make opposing votes less valuable, either by diluting them in a voting district (“cracking”) or concentrating a super-majority in one district (“packing”) to weaken that party in surrounding districts.
Tapp’s paper suggests improvements to the efficiency gap, what he calls “the relative efficiency gap,” that improve its results in races where the population leans heavily for one party.
“It wasn’t a problem in Wisconsin because the vote was nearly 50-50," he says. "But I wanted to do what you do in mathematics: find the beautiful generalization that encompasses the extreme cases, generalizes to broader settings, and tells a more accurate story.”
As for Pennsylvania’s redistricting, Tapp approves of the work that was done from a mathematics standpoint.
“Pennsylvania did a great job,” says Tapp, who lives in a district that effectively didn’t exist before the new map was introduced. “Pennsylvania is the success story. It’s the only time in U.S. history that a map has been overturned due to political gerrymandering and a new, fairer map has been put in place by courts.”
Tapp says the research is moving quickly and already the efficiency gap is losing relevance as it’s replaced with newer statistical methods to assess district maps.
While it’s important to be able to assess the amount of manipulation, the first order of business should be to draw fairer maps in the first place. Tapp, who points out that both parties have engaged in gerrymandering when in power, is a proponent of nonpartisan commissions in which both parties are represented product.
“The idea is not to let the mathematicians draw the map and definitely not to let the computers draw the map. The map should be drawn by a non-partisan commission of people who know the state or the region,” Tapp says. “People who know the region can draw maps that respect communities of interest and natural boundaries. Then you can hand it over to a mathematician to weigh in on whether the map is fair in a partisan sense and if it isn’t, to go back and do it again. That is the role math is playing and should play.”
Taking part in the conversation has given Tapp something else: hope.
“Mathematics feels hopeful to me,” he says. “Applying beautiful mathematics to social problems and to improving the country, I love that.”
Kevin Donahue is a Philadelphia-based writer and editor.