Could Mathematics Save Us From Partisan Gerrymandering?

If the Democrats have a realistic chance of gaining back control of the government, one of the first battles it will have to win is the one against gerrymandering. Though cases about redistricting tend to go either in court, one Tufts University professor thinks she may have a winning solution: math.

Moon Duchin, a mathematics instructor with an expertise in geometry, spoke to the Chronicle of Higher Education about a summer class she devised specifically to prepare mathematicians to testify as experts in redistricting court cases.

Originally, Duchin thought she could be most useful collaborating with state redistricting committees to work out fair district lines. Then she realized that the powers that be often intentionally don’t want to create fair district lines, so her input would easily go ignored in the states that needed it the most.

Hence, she changed her focus to host a class to train mathematicians instead. The class isn’t so much about drilling students with her particular point of view on this subject, but assembling astounding mathematical minds to discuss this issue and work out potential math-backed solutions to the gerrymandering problem.

“When I started thinking about this, I was surprised to see that even though there were different mathematical attempts at a definition, you don’t ever see mathematicians testifying in court about it,” said Duchin.

After all, partisan powers are already using plenty of math to rig the system. Since each congressional district in the state has to be roughly equivalent in population size, politicians will find a way to draw the lines so that one particular party affiliation has the majority of voters in the majority of districts. It’s a complicated mathematical formula to ensure that one party gets the maximum number of representatives with the fewest number of votes.


Photo Credit: Washington Post

When districts look like the examples above, it’s pretty obvious that legislators were trying to cram a particular demographic of people into a single district. However, courts have had trouble legally determining what a “compact” district should look like. That’s where geometry can enter the picture to demonstrate how compactness works from a mathematical perspective.

By Duchin’s own admission, one of the biggest challenges will be for geometry specialists to communicate the mathematical principles to those without degrees in mathematics. A professor could present a highly technical theory well amongst her peers, but that wouldn’t necessarily make it a winning argument for a jury or judge that can’t follow the logic.

To see which ideas people more easily grasp and which need further explanation, Duchin has been practicing discussing these concepts with various audiences (high school students, politicians, a public open forum, etc.) Developing the language to discuss the mathematics to a mixed crowd will be one of the class’ key focuses, and then the students can take that language to court.

“I don’t have any illusions that we’re going to settle that debate forever, but I think we can make a contribution to the debate,” said Duchin.

Duchin has good reason to think so, too. Last year’s federal court case Whitford v. Gill, set precedent by determining that the district lines in Wisconsin had been intentionally devised to benefit the Republican Party, and that legislators had no good reason for drawing their boundaries in that manner other than to manipulate that outcome. The plaintiff used a mathematical equation to demonstrate that this unfairness had occurred.

With any luck, the courts will continue to agree that mathematic principles are an unbiased way to judge the compactness of districts, thereby rejecting some of the inherent partisanship of allowing legislators to draw their own district lines.

Photo credit: Thinkstock


Marie W
Marie W1 years ago

Thanks for sharing.

Herbert C
Herbert C2 years ago

heather g That's the problem, who's independent? Several states have set up "independent" commissions to handle redistricting, but the districts still reflect attempts to balance political parties favoring one party or the other. Another option is to use a computer to draw the district lines using pre-agreed upon attributes and weighting. As Dan B pointed out many districts were gerrymandered to ensure minority representation, no matter how you do it someone will cry foul.

heather g
heather g2 years ago

These districts look ridiculous - it's definitely a job for an independant authority (if there is such a thing)

John B
John B2 years ago

Thanks Kevin for the excellent article and very relevant links. Great concept.

Quanta Kiran
Quanta Kiran2 years ago


Dan Blossfeld
Dan B2 years ago

It seems that this is one article upon everyone can agree. We all think that the political parties should not be drawing the congressional districts. A nonpartisan committee should be taxed with this role. Many seem to think that they should be drawn in the most compact geographical area as possible. This would likely reduce the number of precincts, as the remote arms of the worse gerrymandered districts disappear. More polling places could be established closer to the voters.

One issue not mention is the voting rights act of 1965. Many districts were gerrymandered to ensure minority representation, where they otherwise, was none. The majority-minority districts were drawn to ensure at least one district, where the minority had a majority, and hence a greater chance of representation. This has created "safe" minority districts, which have overwhelming minority populations, not just a simple majority. Many feel that the total elimination of gerrymandering will reduce minority representation. While I would like to see gerrymandering completely eliminated, this argument has merit.

Danuta W
Danuta W2 years ago

Thanks for sharing.

Margie FOURIE2 years ago

Okay. Quite agree with Herbert C

Herbert C
Herbert C2 years ago

The challenge here wouldn't be getting people to understand the math (they wouldn't) the problem of gerrymandering is that you’re asking people who benefit from it to correct it. Not likely.

Freya H
Freya H2 years ago

We definitely need to reform our entire electoral system. A non-partisan committee is a good idea, but remember that it comprises venal and prejudiced humans. Even if you write a computer program to draw more equitable election districts, remember that a human mind creates the program. Democrats are just as guilty of gerrymandering as Republicans.