American Scientist

The mathematical task of deciding what is provably fair can be a daunting one, and even just a few years ago mathematician Theodore P. Hill wrote that for gerrymandering, "there is still no widely accepted fair solution" (also see Hill's article for an explanation of where the term "gerrymander" came from). But at last month's American Association for the Advancement of Science (AAAS) meeting in Seattle, researchers reported on new mathematical and statistical tools that make it easier to detect gerrymandering when it happens.

The timing coincides with this year's decadal census, which itself has its own mathematical history of apportionment for the United States House of Representatives. But once that apportionment is made, the U.S. Constitution (Article 1, Section 4) makes it the responsibility of each state legislature to draw its own electoral maps, identifying the distribution of various constituencies.

Still, states must follow the federal Voting Rights Act of 1965, which prohibits voting practices or procedures that discriminate on the basis of race (racial gerrymandering). So, as the three researchers who presented at the AAAS meeting on the topic put it—both in their presentations and in our follow-up interviews (included in the podcast, below)—the new mathematical and statistical tools they've been researching do make it easier to spot racial and political gerrymandering. But it takes political will to end that practice.

Transcript

Robert Frederick
This year, 2020, the U.S. Census will be getting underway.

[Music starts]

Among other things, the census will determine how many representatives each state sends to Congress. But who gets elected to fill those seats may be gerrymandered with electoral maps drawn to favor candidates based on political party.

Moon Duchin
I think there’s a really interesting moment to look systemically at the way we do different levels of election in the country and to think about changing the rules to comport better with the ideals that we want to have in place. If proportionality a goal, we should write it into the rules.

Robert Frederick
On this episode of the American Scientist podcast, using mathematics to discover and possibly put an end to gerrymandering. I’m Robert Frederick.

[Music ends]

Robert Frederick
The subject of dividing things fairly goes back to ancient times. “I cut, you choose” is a classic solution for how two people might divide up, say, a loaf of bread. But most things that we want to divide fairly aren’t so easy to split. As it happens, in some of these dividing-things-up-fairly problems, mathematicians have shown there’s no solution at all.

Moon Duchin
There’s this whole kind of math or economics called “social choice theory,” which says the system has consequences.

Robert Frederick
Moon Duchin is a mathematician at Tufts University who studies how electoral districts are drawn.

Moon Duchin
The Electoral College system definitely has consequences that are different from what would happen if you went to a popular vote. But there are also theorems that say that no systems has all the properties that you want. And so I think there’s a really interesting moment to look systemically at the way we do different levels of election in the country and to think about changing the rules to comport better with the ideals that we want to have in place. If proportionality a goal, we should write it into the rules.

Robert Frederick
That’s because our system in no way was designed to produce proportional representation, says Johnathan Mattingly, a mathematician at Duke University who works to quantify gerrymandering.

Johnathan Mattingly
... which begs the question, if it wasn’t designed to produce proportional representation, what would the outcome be for a given map with a given set of votes, typically? Or, more importantly, if you had a certain set of votes, what would be the typical outcome if you had drawn non-partisan maps, un-gerrymandered maps?

Robert Frederick
That question, it turns out, is really hard to answer mathematically. And there’s also the question of following the law. The Voting Rights Act of 1965 makes it illegal to produce electoral maps that discriminate by race. Of course, sometimes minority communities are still split up by electoral maps. But if doing so would affect the results of an election, the practice is called “minority vote dillution” says Matt Baretto, a political science professor at the University of California – Los Angeles.

Matt Baretto
The Voting Rights Act of 1965 has provisions which ensure the protection of the minority vote. Specifically, the voting rights act prohibits districting plans that use racial gerrymandering that dilute minority opportunities—opportunities to elect candidates. The question is that detecting minority vote dilution can be quite difficult.

Robert Frederick
These three researchers—Duchin, Mattingly, and Baretto—were speaking at a news conference at the AAAS meeting in Seattle in February on new mathematical tools to detect gerrymandering and to put an end to it. I also spoke with each of them separately. Again, Matt Baretto at UCLA about another dimension to the racial gerrymandering problem.

Matt Baretto
If the community is large enough in size to command a district, that is, they could potentially win up to 51% of the vote in a district, then the Voting Rights Act, separate from the redistricting that happens every 10 years, but the Voting Rights Act of 1965 suggests that we should attempt to draw a district if a group is large enough in size to influence a district. And so that’s when you then have to go into the ground and talk to stakeholders, you have to look at all sorts of voter results and vote returns to see if the group will be cohesive and vote together. If they aren't, if they're too fractured, then the district won't perform.

Robert Frederick
But vote together on what? Federal elections for congressional seats? State legislative elections? There's no one map to rule them all.  And it’s a bewilderingly complicated problem mathematically, particularly because not everyone votes in every election. So I asked the panel if compulsory voting might help, meaning everyone has to vote as is done in Australia, for example. Well, in terms of gerrymandering....

Moon Duchin
With compulsory voting it gets worse...

Robert Frederick
Again, Moon Duchin at Tufts university.

Moon Duchin
...because it gives you greater knowledge of who will vote, so a greater ability to precision engineer your districts.

Robert Frederick
But, Duchin says, it’s definitely a problem that math can help solve—to spot gerrymandering when it happens and to help eliminate it, at least when there’s political will to eliminate gerrymandering.

Moon Duchin
When I started thinking hard about redistricting—so I started working on this pretty full time in 2016—and at that point I thought “Oh, this must be settled math.” In fact, I thought “I’ll just find the best book on it and teach it.” And then the more I got into it, the more that I was like, “Wait a second, this area could really use some more research-level math.” Thankfully there are people already working really hard on that.

Robert Frederick
And Duchin herself has been researching ranked-choice voting, where you don’t just choose one candidate for an office, but rank them in order of your preference. Now, specific procedures vary by jurisdiction, but the idea is that the candidate who has the highest overall preference wins the election.

Moon Duchin
The problem with ranked-choice, it’s extremely hard to model. And even though it’s taking off around the country—so everywhere from Minneapolis to Memphis to the whole state of Maine now—we don’t have enough data on how people list their preferences to train, sort of, standard statistical models.

Robert Frederick
And a particular feature of ranked-choice voting that Duchin says is of interest?

Moon Duchin
Particularly, folks are coming to our group and asking us questions about the voting strength of communities of color. Ranked-choice is thought to be really promising for getting better proportionality.

Robert Frederick
For now, overall, the mathematical approach to spotting gerrymandering that has been prominent in court cases has to do with generating lots of electoral maps.

Johnathan Mattingly
...which help you understand when one map has unusual features or behaviors.

Robert Frederick
Again, John Mattingly of Duke University. And those unusual features or behaviors? That’s a sign that map may be gerrymandered, because it differs so much from all the others generated.

Johnathan Mattingly
The non-partisan scientific question embedded in that statement is ‘How do you generate those large number of maps?’ There’s been a lot of work in how to understand interesting ways to produce maps using Markov-chain / Monte Carlo and other ideas around that.... This method has proven to be particular powerful or convincing in Court—it was one of the Common Cause vs. Rucho case that went to the U.S. Supreme Court—where it was eventually decided not that the facts were wrong, but that the case was not one that the court was willing to take up. Then it returned to North Carolina and this fall in two different court cases all three of the maps typically used at the statewide level—the U.S. Congressional maps and the two maps used in the state legislative assemblies—were thrown out.

Robert Frederick
And so the residents of North Carolina are voting with new maps for the 2020 elections, which started off as maps that had been computer-generated.

Johnathan Mattingly
They actually took a map and then explained every time they wanted to make a change: I have a motion, I want to do this because of this. And I liked that kind of public record of thought, of justification. I liked that.... What I’m against is computerized redistricting.... you know, there’s always going to be questions we were talking about, communities of interest, and minority-majority questions, and, you know, socioeconomic questions. I think those are all important and I think we have to take those into account to have the democracy we want.

Robert Frederick
Redistricting has come a long way from getting out a state map and a pen and literally drawing districts on them, says Matt Baretto. Now, there are even people working on mapping tools to enable the public to help.

Matt Baretto
...that will essentially crowdsource this, that will allow people in their community to report data at the community level, to report where they think their community boundaries are. I’ve seen some, you know, apps that people can download on their smartphone and then draw a, you know, a circle around where they consider their community or their district. And then those all get uploaded and merged together. And so we can actually now hear from people in the community what their perspective—where do they think district boundaries should be drawn. You then do need to use the mapping software, the social science and the statistics to say “Well this is possible; this other district may not be possible; this would violate the Voting Rights Act," et cetera. But the availability of a lot of these tools down just to the average person on the street is, I think, will be widely used in 2021 and it will be really exciting. Some of it might be challenged because it’s new. But I think it will be widely used and I think it will inform a more democratic districting process in 2021.

Robert Frederick
But whatever happens with redistricting, maps, better data, ranked-choice voting, new software apps and crowdsourcing, there’s one factor that really can’t be accounted for. And math isn’t going to solve it.

Moon Duchin
And the factor is who runs in the first place.

Robert Frederick
Again, Moon Duchin at Tufts university.

Moon Duchin
So there are efforts in a lot of places to do candidate training and recruitment. I think that’s just vital, because when you have more different kind of choices, not only can you model elections better, but you can be happier with how they turn out.

[Music starts]

Robert Frederick
You’ve been listening to a podcast from American Scientist magazine, published by Sigma Xi, The Scientific Research Honor Society. For more on the math of gerrymandering, visit AmericanScientist.org and search for “gerrymandering.” I’m Robert Frederick. Thanks for joining us.

[Music ends]