Gerrymandering, or dividing an area into political units to give special advantages to one group, is often used to sway the outcome of elections, but mathematicians may be able to solve the problem. 

According to ProPublica, Austin offers an example of gerrymandering —  the city is carved into six districts to dilute the generally more liberal votes that come out of it. This could potentially impact the elections currently underway in Texas.

Last month, UT hosted a “Geometry of Redistricting” workshop, organized by Andrew Blumberg in partnership with the Metric Geometry and Gerrymandering Group, MGGG, at Tufts University. Presenters at the workshop ran a hackathon and educated the public — and experts in mathematical and statistical fields — about the issue of gerrymandering and the path to a solution that mathematics can offer.

“I think the workshop was really nice in terms of generating enthusiasm and activity,” Blumberg said. “There were a lot of interesting talks by lawyers and political people. For technical people who are interested in political advocacy, that’s going to be very valuable going forward.”

The workshop included two days of a hackathon and map-making sessions, followed by two days of public talks and discussions. It attracted participants from a range of backgrounds, many from outside the field of mathematics. A total of about 150 to 200 people attended the workshop.

“We had about 100 people for map-making, and that was from all over the map — no pun intended,” Blumberg said. “We had people from the water commission in various small cities in rural Texas, and we had students and geography graduate students and people from the League of Women Voters.”

Mira Bernstein, a researcher at Tufts University and founding member of the MGGG, said she sees a problem with America’s system of redistricting, which is different from that in the many countries that use proportional representation.

“The math is a very integral part of all of this,” Bernstein said. “There is a big problem in that the people who are doing policy or citizens who are advocating don’t understand the mathematical aspect. The math we use is not sophisticated math. But math cuts through some of the confusion.”

Blumberg also said there are lots of ways mathematics is relevant to the problem of unfair redistricting. 

“A lot of times, people worry about whether or not the districts are compact in some way,” Blumberg said. “You can look at the ratio of the perimeter to the area. That’s in the positive direction, saying, ‘What should districts look like?’ There’s another direction, which has been very influential lately because (of) recent activity in the courts, … finding tests that say, ‘This particular redistricting plan is probably the result of partisan intent.’”

An example of this type of measure is the “efficiency gap,” the difference between the parties’ wasted votes in an election divided by the total votes cast, according to Nicholas Stephanopoulos and Eric McGhee in their 2014 paper, “Partisan Gerrymandering and the Efficiency Gap.” Bernstein said this approach is flawed, despite press attention.

“The way that people are thinking of mathematicians being involved is coming up with gerrymandering standards,” Bernstein said. “There’s a new standard that is somehow getting no press at all, that we view as the more mathematically robust: extreme outliers.”

With this method, the distribution of votes in a map is compared to computer simulations of thousands of alternative maps, according to an article by Moon Duchin, a mathematics professor at Tufts University who started the MGGG, and Peter Levine, Tufts University associate dean of research. If the map gives an abnormally large advantage to a party, it is considered an extreme outlier.

Common gerrymandering tactics can be challenged by math-informed analysis, but Blumberg said that partisan gerrymandering is ultimately a question of political will.

“What I’d like to see is that most states use independent redistricting commissions and that they use certain suites of tools to make sure that they’re drawing maps which accurately reflect some notion of the intent of voters,” Blumberg said, “And, at the very least, aren’t drawn by someone who has a serious stake in the outcome.”

With Texas in the middle of elections and political activists anticipating redistrictings set for 2021, Bernstein said that the new maps will need to be watched, not just by political activists but by those with a mathematical bent as well.

“Our hope is to get people who have quantitative skills to be involved in this,” Bernstein said. “We feel that people who are mathematically trained and (who) know the background of the issue and are distributed throughout the country can make a contribution. It will be happening all at once and very rapidly, so planning needs to start now.”