How Often Does Redistricting Occur – A new approach to how the Census aggregates its data could make extreme manipulation more difficult, says Moon Duchin.
The word “gerrymandering” conjures up an image: district maps that look less like a tangible community than a Rorschach blot, perhaps one that suggests a “broken-winged pterodactyl,” as a federal judge in Maryland’s Third District referred to it. Read a line like that, and a certain intuition kicks in: There must be something wrong here.
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“While poorly formed districts are a pretty successful flag that someone was trying to do something, they don’t really tell us what their agenda was, or whether it was nefarious or benign,” says Moon Duchin, a mathematician at Tufts University and an expert in gerrymandering. “Bad ways are not necessarily bad, and good ways are not necessarily good.”
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For the past five years, Duchin has led the Metric Geometry and Gerrymandering Group at Tufts, a lab that has quietly changed the conventional wisdom about how gerrymandering works by approaching the issue less as a political problem than a mathematical one. As the country enters a new redistricting cycle, understanding redistricting in those terms has taken on new importance, especially in light of a controversial change in the Census Bureau data that will be used to draw the new district maps.
This year, for the first time, the Census Bureau added random noise to its data that makes it slightly inaccurate at the smallest and most zoomed-in level, but accurate at an aggregated, wide-angle view. The approach, known as “differential privacy,” aims to protect the anonymity of census respondents amid an abundance of third-party data online that might otherwise make it possible to personally identify census respondents. The move has sparked a wave of criticism that redistricting based on those “noisy” numbers will be inaccurate.
Duchin, who has studied the Census’s use of differential privacy over the past year, came to a different conclusion: that, in terms of drawing districts and enforcing provisions of the Voting Rights Act, the effect of noise is negligible. But, to his surprise, Duchin also found that this noise could make extreme gerrymandering in new districts more difficult, potentially complicating supporters’ designs for 2022 congressional maps.
“If you build your district starting with the smallest particles, that is, if you do the practices that are associated with gerrymandering and make micro-detailed plans, [differential privacy] is going to mess up your numbers more than if you start with larger units. and only use the small units to tune in at the end,” Duchin said.
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What is there to redistribute in the coming months? How does math change the way we should think about gerrymandering? And what is the difference between neutrality and fairness in map designs? To break it all down, Magazine spoke with Duchin via Zoom. Below is a condensed version of that transcript, edited for clarity and length.
Q: Many people approach redistricting from a policy-based perspective. You come to it with a foundation in math. There’s a temptation, when we think of math, to see it as a kind of “neutral,” as if approaching redistricting from a mathematical perspective based on hard data could make it an objective exercise. How do you think? Is there an objective way to draw districts?
Moon Duchin: We’ve been redistricting since the American democracy was founded. Originally, there was this idea that if you want a deliberative democracy, if you want people to actually be able to come together and talk about things, then a big nation makes it harder to do that. So having states within that nation—and then districts within those states—was a way to create a network of democracies.
But then you have to ask yourself: What would [drawing districts] optimally mean? Whenever I talk about redistricting with quantitative people, this is something they almost invariably think of, implicitly or explicitly, as an optimization problem: you take the rules, you write them down, you find the best plan. But if you add some nuance to that conversation, you realize that this “optimization” problem is probably intractable, and not the most productive framework anyway.
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In the 1960s, the Supreme Court said, “We’re going to engage in redistricting.” And his first speech was what we now call “one person, one vote”—the idea that we should really balance the population of the districts. That was a great moment of opportunity for computers. If you’re just drawing districts with pencil on paper, it’s extremely difficult to balance the population very closely; you want a computer to come in and you can do that. So if computers are going to be involved, the question is: how?
If you look at many newspapers from the early 1960s, you will see that people thought computers could go in and find the “best” district plan. But you still have this big question: What would it mean to be the “best” plan? Population balance is one thing, but you want your districts to be connected and maybe you want them to be in good shape and so on. And then, suddenly, this increasing complexity establishes the dream of “optimization”.
If you were trying to find the best and most balanced population plan possible, at the scale of the US. US, that’s not a computer problem where you simply need a faster computer; that’s a computer problem that you’re just not going to be able to solve, because, first, there’s no agreed-upon definition of the “best” plan, and, two, if you could stipulate a definition, this kind of problem is thought to be permanently out of reach of the computers to solve exactly. Also, even if you could create a large unified “goodness” score for a district plan and get a computer to find the map with the best possible score, does that really become a reason to enact that map? If a map has a better “goodness” score in the seventh decimal place than a million other options, is it really preferable to the alternatives? You have these multiple problems: optimization is not that manageable, and in any case, it’s not obvious that optimization solves the problem. So this may not be an optimization problem after all.
The reality on the ground is that practitioners understand that redistricting is a truly holistic process. It is a process that mathematics should support, but not one that should be outsourced to mathematics. That interaction is delicate.
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Do you think “fair” is the same as “neutral” when we’re talking about drawing district maps?
Emphatically not. That’s a very important point: PCs are very good at “neutral”, but not necessarily good at “fair”. And there is a huge community, even within computing, that recognizes the challenges of equity within a paradigm that is set up for neutrality.
Let me give you a quick example: districts, by themselves, are generally not very good devices for representing minorities. And there’s something ironic about that, because I think that’s one of the main arguments for districts in the first place: that if you have a state and there’s a certain subpopulation that needs representation, you can draw a district in which they have a controlling influence and they can elect representatives. Today, we think it is important, so that racial and ethnic minority groups can elect preferred candidates. But that same concept could apply to people who prefer minority political parties and are geographically clustered enough that you can capture their preferences by drawing a district.
“That sounds like a gerrymander, but it turns out you can’t draw a Republican House district in Massachusetts.”
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The irony is that districts aren’t great at [representing minority interests] if you draw them blindly. An extreme example of this is Massachusetts, where I live. Massachusetts has an incredibly consistent track record: Over the past 20 years, in US presidential and Senate elections, we’ve tended to favor the Democratic candidate by a 2-to-1 margin, about 65-35. There’s a solid one-third of Massachusetts voters who are reliably Republican in this type of election, so when you take our congressional delegation and see that we have nine districts, you can expect a third of them to be Republican as well. But there is none; we haven’t sent a Republican to Washington since 1994.
Now, that sounds like a gerrymander, but it turns out you can’t draw a Republican House district in Massachusetts. If you take one of those 2-to-1 elections and look at where people live, you’ll find that the way people get to the polls is really even; we have a third of the votes cast for Republicans statewide, but they’re also, like, a third of every city and every district. Republican candidates have this huge structural disadvantage because their voters are not clustered. They do not have enclaves in the State; they are really evenly distributed.
A more notable example might be if you look at the Voting Rights Act,
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