Numlock News: August 6, 2025 • Gerrymander, Coin Flips, Sampling
By Olivia Walch
Walt is out on vacation, and filling in today is Olivia Walch, author of the book Sleep Groove: Why Your Body's Clock Is So Messed Up and What To Do About It.
Gerrymandering’s been in the news a bit lately. This is something I spent a lot of time thinking about circa 2017-2022, so I thought I’d revisit the topic again for all the Numlockheads out there.
Nice-looking
Many people hear gerrymandering and think “ugly shapes.” The opposite of an ugly shaped district is called a compact district, and as of 2021, 37 states require state legislative maps to be “compact” (21 require the same of their congressional districts). However, as intuitive as compactness seems, this is actually a pretty antiquated way of framing the problem. The reasons are two-fold: 1) ugly shapes are sometimes required by geography (rivers, mountain ranges, coastlines) or compliance with the Voting Rights Act, and 2) modern computers can find very lovely-looking district shapes that are still wildly unfair. More on that later.
Michael Mcdonald, Yale Law Review
58% of the Vote, 58% of the Seat
A lack of proportionality is the next thing people tend to look for in detecting a gerrymander. If you get 48% of the votes, but 53% of the seats, surely that’s a sign of some malfeasance, right? Not necessarily. Imagine a place where every single household had 3 voters for Party A and 2 voters for Party B. No matter how you draw a district in that state, Party B will never win, despite making up 40% of the vote share — they’re distributed too homogeneously. This is basically what happens in Massachusetts, where no Republican has served in the U.S. House of Representatives since 1997.
Let’s Doubleclick on That Last One
In the case of Massachusetts, we can do the following: take all the building blocks of a district (towns, precincts), sort them by how Republican they were in a given election year, and try to build the most Republican district we can out of these building blocks. This gives up the typical requirement that a district be contiguous (as opposed to, you know, a bunch of tiny scattered blobs all over the map). However, even when we stop requiring that, there are still some election years where it’s impossible to make a Republican district at all in the state. To quote the authors who actually did this work: “Though there are more ways of building a valid districting plan than there are particles in the galaxy, every single one of them would produce a 9–0 Democratic delegation.”
Duchin et al., Election Law Journal
Coin Flip
What about competitiveness? Candidates actually working to win seems like a sign of a healthy system. Indeed, a competitive district is unlikely to be one that a party nefariously gerrymandered for themselves. That said, competitiveness comes with its own baggage: when districts are essentially a toss-up, it means you can end up with some very not proportional results. Consider Minnesota in 2016. Three of the districts were won that year with less than a 2% margin. With barely any change in the statewide vote share, Republicans could have won 25% to 62.5% of the seats (two to five seats) with 48% of the vote. It can make the results either look like an extreme Democratic gerrymander (25% of the seats while 48% of the voters went Republican) or an extreme Republican gerrymander (62.5% of the seats with only 48% of the votes) to proportionality-minded onlookers.
Bernstein & Walch, Political Geometry
Scores Will Not Save Us
So, being disproportionate doesn’t mean you’re gerrymandered, and winner-takes-all elections make competitiveness and proportionality fundamentally incompatible. How, then, can you identify a gerrymander? People have proposed a lot of scores for doing this, some of which have made it before the Supreme Court. One of these is the efficiency gap, which measures the difference in “wasted” votes between the two parties. If you get 49.9% of the vote share, you still lose, which means a lot of wasted votes. Meanwhile, if you win with 50.1% of the vote share, you were very efficient with your votes: just barely enough to win. This seems like a solid approach, but once you poke it, you start to notice some unsatisfying things about the efficiency gap. It can’t handle the volatility of the Minnesota example or the homogeneous distribution in the Massachusetts example, giving weird results when you move away from roughly competitive races. Most importantly, people have already tried pitching it as an anti-gerrymandering measure, and it didn’t convince the Supreme Court.
SCOTUS
Here’s Chief Justice John Roberts: “And if you're the intelligent man on the street and the Court issues a decision, and let's say, okay, the Democrats win, and that person will say: ‘Well, why did the Democrats win?’ And the answer is going to be because EG was greater than 7 percent, where EG is the sigma of party X wasted votes minus the sigma of party Y wasted votes over the sigma of party X votes plus party Y votes. And the intelligent man on the street is going to say that's a bunch of baloney.”
Sampling Might
I consider a gerrymander to be a kind of map. The kind that would produce extreme outlier outcomes compared to the ones you get from uniformly sampling billions and billions of maps that satisfied the districting criteria and laws of the state in question. This approach works for the Massachusetts (you’d basically only get 9-0) and Minnesota (coin flip-like results would be typical) examples above. It can handle the fact that a very nice-looking (computer-generated) map could produce very atypical (gerrymandered) results, and it accounts for the geography and demography of a state that together determine the space of what’s possible. For a taste of how big these spaces can be, consider the 4-by-4 grid: There are 179 million ways to label those squares as belonging to district 1, 2, 3 or 4. Uniformly sampling this space is a challenge, but it’s the only choice you’ve got — enumerating every map is out of the question.
Moon Duchin, Political Geometry
Check out Sleep Groove: Why Your Body's Clock Is So Messed Up and What To Do About It
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