Moon Duchin, mathematician and associate professor at Tufts University, visited The Spence School recently to talk to students about the math behind gerrymandering. Dr. Duchin, who received her Ph.D. in mathematics from the University of Chicago, has been a vocal advocate for using technology in evaluating cases of gerrymandering.

 

Isabelle R. ’19, who introduced Dr. Duchin at the Upper School assembly, noted that it was an opportune time to discuss biased redistricting.

 

“The United States Supreme Court is hearing a case entitled Gill v. Whitford, which could fundamentally change the way we create congressional districts in this country,” Isabelle said.

 

Dr. Duchin provided an overview of what gerrymandering is—essentially creating designer districts to obtain a certain political advantage—and its origin with Elbridge Gerry, a governor of Massachusetts who arranged a district in a way to keep his party in power. A newspaper satirized his map in a political cartoon and suggested his district looked like a salamander, which, along with the governor’s last name, created the term “gerrymandering.”

 

Dr. Duchin also defined “the tools of the gerrymander,” which are “packing” and “cracking.” Packing puts like-minded voters into one district, which can help the other party win the remaining districts. Cracking disperses the like-minded voters across multiple districts to prevent them from establishing a majority. She showed one map illustrating that while Wisconsin is made up of roughly 50-50 Republicans and Democrats, the GOP holds two-thirds of the seats. (Dr. Duchin emphasized that both Republicans and Democrats gerrymander whenever they can.)

 

There are many factors to consider when redrawing districts, such as compactness, population equality and contiguity. Generally, district maps are also supposed to have a nice shape to them, though many of these terms have conflicting or ill-defined definitions across state lines.

 

“Weird shapes tell you somebody is trying to do something, but they don’t tell you what it was,” Dr. Duchin said.

 

Dr. Duchin gave two examples from the 1950s and ’60s where irregular district shapes were shown to be disenfranchising black voters in Alabama and Mississippi. In other instances, a party may want to set up “safe seats” that the incumbent can easily win.

 

One way to examine the compactness and efficiency of shapes is through an 1842 isoperimetric theorem, however, not surprisingly, Dr. Duchin said she wants to modernize how we look at redistricting.  

 

“Computers can’t possibly follow all those rules I told you about, so you can get a computer to take into account the ones that sound ‘mathy,’ and then you can try to optimize,” Dr. Duchin said, noting that while a supercomputer like Blue Waters can be used to help tackle gerrymandering, it still does not know how to take into account things like trade-offs and priorities.

 

“We don’t want computers to take over,” Dr. Duchin added. “We want to use computers as a tool. Computers are never going to think about fairness for us. That’s a fundamentally human endeavor.”

 

One way to use computers as a tool is through a Markov chain to consider all the different ways to draw a map. Dr. Duchin talked about one algorithm that Duke researchers used to find nearly 20,000 different redistricting plans in Wisconsin. What they learned from comparing these iterations was that the state’s chosen plan was an outlier that widely favored the Republicans. Dr. Duchin noted that there is a chance that this method of looking at outlier plans will factor into the Supreme Court decision on Gill v. Whitford in February.