Is There a Fair Way to Divide Us?

At first glance, my guest today, Moon Duchin, looks like a fairly typical example of a successful professor of mathematics. She teaches at Cornell University, having built her academic reputation by working on incredibly abstract ideas in geometry. But Moon has done something way beyond the typical. She managed to find a very practical application for her abstract ideas in the area of political gerrymandering. And since then, she’s worked on the ground with state commissions and courts to transform the way redistricting is done.

DUCHIN: We don’t have a baseline. We don’t know what normal districting looks like. And what the math folks have brought to the table is better and better methods for sampling from that huge, unthinkable wilderness of plans.

Welcome to People I (Mostly) Admire, with Steve Levitt.

Moon Duchin first saw the unexpected connection between her geometric research and gerrymandering when she taught an undergraduate course on the mathematics of social choice in voting. This is a kind of class assignment every professor tries to avoid. It’s so much work to prepare a new course in an area you aren’t already an expert in, and professors tend to like to teach upper level courses because there are fewer students and the material’s more challenging. I started our conversation by asking her why she let herself be drafted to teach an entry-level course far from her area of expertise.

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DUCHIN: Actually, I wasn’t so much drafted as I drafted myself. At the time, I was trying to work my way through the entire undergrad curriculum and teach all of our classes. 

LEVITT: Why would you want to go through all of the undergraduate classes? That sounds like the opposite of what most faculty are trying to do.

DUCHIN: It is the opposite. But I love learning things through teaching them, and I love stretching across the math curriculum. This was a class that was really being presented for non-majors. And so this was a really popular way for people who didn’t like math much to take a math requirement. What surprised me is that it was sneaky deep. It actually didn’t even seem easy at the first level of approach. As a little add on at the end of the class, I had gone through all these theorems about how voting works and doesn’t work and then wanted to pivot towards something that looks a little bit more like the American system. And by the way, I was teaching this class in 2016 when there was a really weird primary going on when this guy named Trump was getting a bunch of votes as you rolled through primary states. And so there was a lot happening and I wanted to try to connect the theory to some of what was actually going on. So for that you really need the story of redistricting, which is when you take the country or take a state or take a county or any kind of jurisdiction and you divide it up into pieces, each of them, to conduct an election. And then when you have to redo it regularly, you’re redistricting. 

LEVITT: And in the U.S. a census is done every 10 years, and then we reallocate seats across states. That’s when we see the most redistricting because Massachusetts might gain or lose a seat and California gains or loses two or three. So you have to redistrict in order to do the next election.

DUCHIN: Yeah, funnily enough, that rule that you have to redistrict when the new population numbers come out, that only comes from the 1960s. Before that, states that didn’t see their apportionment change — you know, if their number of districts stayed the same, they just left their districts in place even though people were moving and population was shifting. But since the ‘60s, the Supreme Court steps in and says, “No, every time there’s a census, you need to rebalance.” So as you say, that’s when most of the redistricting scrum happens.

LEVITT: Did you see right away that the very difficult math tools that you were developing in your own research, that they had a very natural application to the question of gerrymandering?

DUCHIN: No, it took quite a while to see how my math was going to bear on redistricting. So the order that this goes in my life is: I teach this class, I want to put a little gerrymandering content at the end, I look for the — what I’m sure is going to be the well-solved literature, and then I find that there’s still a lot to be done. And then gradually I realized that my math toolkit can help. So I come to this as a research problem in this funny, circuitous way. But pretty much as soon as I did, I realized that there’s some real geometry in this, which has to do with distributions. So you have people unevenly distributed over the territory of the U.S. and the territory of each state. And then within the people as a whole, you have subgroups that are really important for political representation. And some of them are more concentrated and some of them are more spread out.

LEVITT: Okay, so gerrymandering, which has got to be perhaps one of the weirdest words in the English language, means what?

DUCHIN: Great word, yeah. That’s just basically abusive redistricting. So the idea is: you have the power to draw the lines and you use that power to advance some agenda. Notice, that’s slippery, right? That just basically says, “I don’t like the way you redistrict it.” It’s really quite hard to specify exactly what’s meant by that. I would say the broadest consensus is that if you’re in control of drawing the lines for some seats, some representation, then Gerrymandering is where you use it to get more seats for one kind of representative at the expense of others.

LEVITT: Okay, and the name, can you give us a little history lesson — it comes from Elbridge Gerry, right?

DUCHIN: Yeah, who said his name “Gerry,” actually, as far as I understand. I just moved here to Ithaca from Cambridge where everything’s still named for the guy.

LEVITT: Because he was the Governor of Massachusetts at one point?

DUCHIN: He was indeed, at the time of the 1810 census. And he approved a set of lines for the state senate map which had a district on the north shore that people didn’t like. And it was thought to be a partisan gerrymander where one side was the Democratic-Republicans and the other side was the Federalists. By putting together towns in this configuration, he was accused of putting a thumb on the scale. A political cartoon, a pretty famous one, like a woodcut political cartoon, was created in the years after that census showing that district with artistically rendered wings and teeth and claws. And it was called Gerry’s salamander. And that’s what became “gerrymander.”

LEVITT: What’s weird is that I’ve seen that picture and it looks like a dragon because salamanders have no wings. It’s interesting they called it a salamander.

DUCHIN: Maybe just because gerry-dragon doesn’t have the ring to it. Not quite sure. But yeah, the other thing that’s really striking when you look at it today is that it looks just fine. It’s actually whole towns. It doesn’t even cut — it’s below the town line, let alone cut into precincts and cut into neighborhoods. It doesn’t really look so bad from a modern perspective. But the kind of polemical language that accompanied the cartoon was all about skipping over some population to grab other population. And a lot of its snaky shape, it’s up there at the northern border of the state, so it seemed unnatural with respect to how it was dividing up the North Shore towns.

LEVITT: Now just to be clear, the potential value to a political party of controlling the redistricting process, it can be huge. So let’s just take a simple example. Let’s say there’s a state that is 59 percent Democrat and 41 percent Republican. And let’s say it has 10 congressional seats. If the only constraint on how districts are constructed is that each district has to have the same number of voters, and if I’m doing the math right, you can come up with a redistricting plan that gives that Republican minority anywhere between zero representatives out of ten and up to eight representatives out of ten. Can you explain how that works?

DUCHIN: Yeah, first I agree with your math. But yeah, the reason is we’re using a really, like, sharp-edged rule, which is just whoever has the most votes.

LEVITT: That’s our electoral rule is that small differences in vote shares lead to very stark differences in outcomes. One person wins, it’s winner take all, essentially.

DUCHIN: Exactly. Binary outcomes. So sometimes that’s called “first past the post.” And so, to control a district, you just need half of its votes plus one, in this kind of simplified two-party scenario. And so, you can control eight districts by just having — in each of those, you just need 50 percent of the district plus one — just a hair over 40 percent of the votes can control eight districts.

LEVITT: The nomenclature that political science use, I think, is “packing and cracking.” So in this case, you pack all of the Democrats into two completely Democratic districts. And then that leaves eight districts, which are almost even, but tip just in favor of the Republicans.

DUCHIN: Exactly. That’s packing and cracking. Economists would think of this as a notion of efficiency. And so if you’re in charge, you give yourself really efficient wins, and then you stuff a bunch of wasted votes of the out group into a few districts. You’ve packed them into some districts that you’re willing to lose, and then you’ve cracked them by splitting them across the districts that you want to win. I should mention, though, that packing and cracking are the most common, but there are also notions of stacking, and there’s even fracking. The inimitable political scientist Bernie Grofman came up with that one.

LEVITT: Okay, so our simple example, the only constraint we put on was that the districts were equal size. But in the real world, what are the rules around redistricting?

DUCHIN: Oh, it’s so complicated. One of the things you learn when you start doing the actual kind of consulting work, is that the rules, they’re not terribly clear. And certainly they don’t come with a priority order in most cases. But I would say there’s a big six of what the rules tend to be because they vary state to state. The only two that are universal around the U.S. are population balance and some sort of web of rules around racial fairness. There’s the Voting Rights Act of 1965 that’s still federal law while we have it, because the Supreme Court definitely has sights on that law. And there’s also racial fairness jurisprudence that comes out of the 14th Amendment, which is equal protection. The idea that race shouldn’t predominate when you draw districts. And then there are four more, briefly. Two of those are mathy sounding. One of them is that the district should be connected pieces, one piece, which in redistricting language is called contiguous. Another is what’s called compactness, which means you want the districts to have nice shapes. You could imagine, when I started thinking about this — because I’m a geometer by training, that’s where I thought, “Oh, hey, maybe my toolkit can be useful here, thinking about: what do we really mean when we want districts to have nice shapes?” I imagine we’ll come back to that. So that leaves two more rules of the big six, and one of them is respect for what’s called political boundaries. That sounds like it might be about partisanship, but here all that means is that for units like counties, cities, towns, sometimes precincts, which are thought of as political boundaries, you want to try to keep those whole, and you don’t want to split any more counties than you reasonably have to. And then the last one, which is maybe the vaguest of all, but I think increasingly interesting for a lot of different people, is called communities of interest. So that one’s the idea that when people have a shared historical or cultural or economic interest, that you want to identify the communities that correspond to that shared interest and take them into account when you draw the lines. And so you can see how slippery that is to operationalize.

LEVITT: Now, what’s notably missing in those rules around redistricting is any strict notion of outcomes. For instance, there could be a rule that says, “If one party received 40 percent of the votes in the last election cycle, then district lines should be drawn so that the party’s expected to win approximately 41 percent of the congressional seats in that state.” But that’s totally absent.

DUCHIN: States have the ability to add rules about partisan fairness, and quite a few do have something in there, either a constitution or just in statute or just in the state guidelines that alludes to partisan fairness. But they’re usually pretty vague. Michigan got something into the state constitution after a 2018 vote that says you shouldn’t unduly favor a political party. So that’s directionally what you’re talking about, but it’s a lot less precise. There’s only one state that I’m aware of that does something like you just said, and that’s Ohio. And that one actually says that you should try for proportionality when you draw your districts, and that does mean what you just said — that 40 percent of the votes should get 40 percent of the seats. The reason that’s a little sad is that even though that’s now in Ohio’s constitution, the people in charge of the line-drawing process were extremely partisan actors in this cycle in Ohio, and they just totally ignored that, even though it’s sitting right there in the constitution.

LEVITT: It seems intuitively that proportionality would be the fair way to do things, and in countries like Germany, that’s more or less how they do it in parliamentary elections because they have proportional assignment of seats.

DUCHIN: Oh, not exactly. So Germany has a really interesting system. But you’re right that most of the world has proportional assignment of seats. That’s called party-list voting. It’s used in about half the countries of the world, if I remember right. And party list says you vote for a party and then seats are filled in proportion to those votes, but the parties maintain a list of who they want to seat. That’s why it’s called “party list.” And just how deep they go in the list depends on their vote support. So that’s very frequently used. Germany actually has a super interesting wrinkle on top of that, which is — first of all, there are single-member districts, and they do conduct first-past-the-post elections. But then there are additional seats that are used to bring those numbers into proportion with people’s party preference. So this is sometimes called a mixed-member system, where some of the members are elected out of districts, and others come off a party list.

LEVITT: And the attractiveness of what we do as opposed to a party list is that you have this real geographic component, and so you represent a particular set of people. Do you see that as a benefit of our system or am I missing the boat?

DUCHIN: No, yeah, it’s actually really interesting. So I would flip it around and say the downside of party list is parties, in some sense, right? It gives a lot of control to the parties. And if you want to see, for instance, diversity in your legislative body, then you have to trust the parties to put it on their list. So many countries around the world use party list, but have a kind of so-called gentleman’s agreement by which the parties agree to have some kind of diversity for, like, relevant minorities in that country. I think that really highlights a flaw of party list if you have to have handshake agreements to make your list diverse. The idea of voting directly for people is probably just generally more attractive in the American way of thinking about our political representation. But as you say, the case for it partly has to do with the salience of geography. Go back to the Federalist Papers and you’ll see the argument that these constituencies around the country are going to have so-called competing local jealousies. And I take that to mean, you have shrimpers in Louisiana. You have loggers in Oregon. You have various kinds of local interests. And those interests might be at the sub-state level. And you want some representation for geographically correlated local interests, neighborhoods, and types of people. That’s going to be the argument.

LEVITT: Yeah. So the first place where some really interesting math starts to creep in here is what one might call the segregation paradox. In general, we think of residential segregation of racial minorities as being bad — a sign of some kind of social problems like discrimination. But in the context of political representation it’s actually good in a sense. Could you explain that?

DUCHIN: First let me just point out that there’s some conventional wisdom here that’s exactly the opposite of what you just said, but I’m going to come back to it and say you’re actually more right than the conventional wisdom. What is said — the conventional wisdom — is that Democrats may be at a disadvantage in redistricting even before anyone starts gerrymandering. They may be at a natural geographical disadvantage because of where they live. And so the logic goes that Democrats pack themselves into cities where they sit really densely, and since they’re packing themselves into cities, they end up packed into districts just naturally. Actually, there’s a wonderful legal scholar named Pam Karlin who’s done lots of work on redistricting among many other things, and I once heard her at a conference say, “It’s because Democrats like to huddle for warmth in the cities that they end up packed into districts.” And so what I would say to that — what I did say to her at the time — is, isn’t this just confusing these two different meanings of the word pack? One has to do with density and the other has to do with inefficiency. And I don’t see that they necessarily have to go together. I’ve spent years trying to tease that out. What I end up thinking is pretty much in line with what you said at the beginning, which is that if you cluster and decluster a minority population, and then you try to draw lots of districts and see if they’re advantageously arranged, if that minority population is advantageously arranged for representation, you’ll find by far the best representation is as they get very clustered. It goes against the conventional wisdom that packing together, that dense arrangements are bad.

LEVITT: I think the intuition I have for it is — let’s say you’re a minority. Take the same silly number I’ve been using the whole time, 41 percent. Let’s say you’re a minority in a state and you’re uniformly spread over the entire state. You’re 41 percent of the electorate everywhere. Then it’s really easy to just draw lines around every geography and you get exactly 41 percent of the vote in every district and you lose every single one. I think that’s the intuition I have for why, if you’re spread too uniformly, and you’re a minority, you’re destined to do poorly.

DUCHIN: Yeah, that’s dead on. So I have a paper where we look at this, and having looked at all 50 states, there’s one state that stands out by far among all the 50 as having the most uniform political geography. And I think it’s a surprise, like I wouldn’t have guessed which state it is, but it’s Massachusetts. You think of Massachusetts as such a blue state, but actually, Republicans are always clearing 30 percent of the vote in statewide contests. And so what that means is, say, a third of the voters statewide prefer Republicans, but that’s also true at every smaller level, right? So if that’s true in the counties and the towns, maybe it’s even true in the households, then what that actually means is that it doesn’t matter how you draw the lines. You’re always going to get an all Democratic delegation. And sure enough, if you look, I think 1992 was the last time a Republican was elected to Congress out of Massachusetts. We love our Republican governors in Massachusetts, but for Congress you’re seeing a sweep. These days it’s 9-0 every two years. Part of the reason is the political geography.

After this short break, Moon Duchin and I return to talk about why it’s so hard to create redistricting plans that are fair.

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LEVITT: Okay, I could see a listener thinking at this point, I don’t really get why we’re going to need Moon’s fancy math. Why’s choosing fair districts such a hard problem? What is it about the problem that makes it a really hard one and one that requires the cutting edge math that you do?

DUCHIN: To answer that, partly I’d go back to this fantastic comment made by Justice Samuel Alito in one of the redistricting cases that faced the Supreme Court recently. I think this was in Rucho, the partisan case out of North Carolina. And what happened there was Alito was musing about how many possible districting plans there are to compare. And he said, “I don’t know, maybe you have 100, maybe you have 25, I guess there’s probably thousands,” he said. And all the math people like me fell out of our seats because, yeah, there are thousands. Actually probably the right scale to think about is a Google — one with a hundred zeros. That’s probably how many districting plans there are to compare, Justice Alito.

LEVITT: We laid out before the rules about what a plan had to have, and there were a handful of them, but states are big, there are a lot of people, there are a lot of cities and counties within them. And what you’re saying is as you start to think about the explosiveness of the number of possible combinations, it goes to infinity really, really fast. So in other words, the possibility space is just too big for humans to think about in any sensible way.

DUCHIN: That’s definitely true. We’re talking, for sure, more than the number of particles in the galaxy. But it’s not just that it’s big, because we can handle big spaces depending on how they’re structured; it’s that it’s big and very hard to explore. Back in the 1960s, you start to see articles coming out, both in law reviews and in technical journals that are like, “Hey, computers are pretty soon going to be able to just search all the districting plans.” This just turns out not to be true. It’s not only that there are so many, but there’s no good recursive structure in there. So that’s a mathematical term, but what I mean is: if you know something about districting a smaller state, that doesn’t help you districting a bigger one. The big problem doesn’t break down into easier ones in a nice way so that you can approach it systematically. So this is where people like me started to get involved because the court’s been saying, how are we supposed to know what extreme gerrymandering looks like if we don’t know what redistricting looks like without gerrymandering? We don’t have a baseline. And what the math folks have brought to the table is better and better methods for sampling from that huge, unthinkable wilderness of plans. And so now we have pretty good ways to get what you’d call a representative sample. Like with polling, once you have a representative sample of the electorate, you don’t have to ask that many people in order to get a sense of what’s going to happen. And this is the same thing. Once you can representatively sample from plans, then you can take a plan drawn by the legislature and see how it looks compared to those. And that gives you a sense of whether someone was trying to take undue advantage or whether it’s just where people live that caused the chips to fall where they did.

LEVITT: So what you’re saying is that in this nearly infinite set of possible districting plans, there’s no easy notion of being able to draw a sample and say that’s representative, because we can’t identify the set itself. And so we have no way to go back and say, how do I know it’s representative when I don’t see all the members of the set. Is that the gist of what you’re talking about?

DUCHIN: Yep, that’s the gist. So we needed some new ideas collectively as a research community for what it would mean to get a representative sample.

LEVITT: Okay, so I know this is hard. It’s hard math. But can you take a shot at explaining what it is you’ve been working on that helps us get to this representative set?

DUCHIN: Yeah. When I started working on this circa 2016, there were algorithms that would run and give you a districting plan, and those algorithms used randomness in their construction process. And so people would say, “Oh, here’s a random sample,” and then treat them as though they were independent. But the problem was, with the methods that were available at the time, you didn’t really know why it was more likely to see certain kinds of plans than other kinds of plans. I like to lean on this analogy to polling an election where you’re like, “Okay, I got this number of men and this number of women who responded,” but I’m probably going to try to correct those shares to look like the likely electorate. I’ll try to reweight them to understand, how many men versus women do I expect to show up on election day? And so the same thing with plans. If I’m getting a lot of plans that have long, snaky districts, and I’m wondering, is that typical? You want to be able to understand why certain things are coming up more than others, so that you know whether you’ve got something that looks like the full body of plausible plans that meet all the rules. So let me tell you just the littlest bit about the math that my research group developed to work on this. There’s this concept in math of what’s called a Markov chain. You start with an object, in this case a districting plan, and then you change to another, and you change to another. And you can visualize this as a walk through the universe of possibilities.

LEVITT: So whatever you had last time, you make one change to it essentially.

DUCHIN: You make one change. That’s right. 

LEVITT: And then you change it the next time and you keep on going, yeah.

DUCHIN: And that’s a little step in this big universe, right? And so maybe in the case of, say, Massachusetts — Massachusetts has 2,000 precincts. So a natural thing to do would be to start with a plan, grab one of those 2,000 precincts, and just move it from one district to a different one. That’s a move. It’s a simple move. And now what if I do that a billion times? Then I might end up with something that looks totally different than what I started with. And looking different is nice, but you want some mathematical control. So when we started getting involved, we realized, actually there’s another good analogy that I think will really help us think about this. Imagine you want to shuffle a deck of cards. You could certainly take a card off the top and put it somewhere random in the middle, and you get a new order. Do that a lot, eventually it’s going to get shuffled. But that is pretty inefficient, just changing that little one thing at a time. So my research group came along and came up with something that’s analogous to the riffle shuffle, where you split the deck in half and just interleave all the cards in a random way. So we came up with a big way to change plans one step at a time. And I can actually say what it is. It’s not that hard to picture. What we said is, why don’t you fuse two districts together that are neighbors? And then draw a boundary in a totally new way. So you see how instead of changing just one little particle, that takes two districts and fundamentally reconfigures them. And then do that a lot. And so we were able to implement that to run really fast and to prove some theorems and get some mathematical control of what happens after a long time and why you’re more likely to see certain kinds of things than others.

LEVITT: Using your methods, you come up with a distribution of what randomly generated redistricting plans would look like in terms of expected seats won by each party. And then when you’re brought in as a consultant, you compare that to the actual plan that has been proposed. And if that actual plan is an extreme outlier, then it’s likely a case of gerrymandering. Is that the gist of it?

DUCHIN: So what I just described where you’re creating this random sample, let’s call that the ensemble method because the collection of plans is called an ensemble of alternatives. And what you just said, outlier analysis, is one thing you can use that for. And courts have definitely found that to be pretty persuasive. If I can show that you’re way in the skinny part of the bell curve, then you’re an outlier with respect to the distribution, so that’s suggestive of some intent to gerrymander. So that’s definitely one application, but there’s others. Let me point to the litigation that happened in Pennsylvania in the last few years as a way that ensembles were used in a slightly different way that I thought was very interesting. In that case, the Republican controlled legislature at the time had put out a plan that actually looked pretty typical of blind plans — I’m going to use blind as a synonym for neutral. That doesn’t mean it’s fair. Because of where people live in Pennsylvania with Philadelphia all the way in the corner of the state, Pittsburgh on the other side, the geography was such that that blind draw of plans was really quite favorable to Republicans, gave a few extra seats to Republicans relative to proportionality. In computer science, fairness might have to do with some axiom of giving things out in proportion, perhaps, to the distribution of other attributes. Fairness might be an aspirational target, and a neutral process isn’t always fair.

LEVITT: Okay. And in Pennsylvania, blind districting plans end up not being fair in that sense because you’ve got all the Democrats packed in the corner of the state in Philadelphia.

DUCHIN: Yeah. I’m pretty used to kind of code switching between talking to academic and non-academic audiences, but I was an expert in this Pennsylvania case. And I remember when I said in the courtroom that blind isn’t always fair, laughs went up around the courtroom. They thought I was joking. Because the people in the room thought, what could be fairer than being blind? You really have to get to this notion that something that’s facially equal between groups might not be allocating resources in a way that’s fair by other kinds of measurement.

LEVITT: Yep. That makes sense.

DUCHIN: So bracketing that just to finish the Pennsylvania story, exactly what you said is the argument that was made by several plaintiffs groups, which was, yeah, the blind process would give you a certain range of representation, but in Pennsylvania you have a free and fair elections clause, and so shouldn’t you be trying to do better than blind? If it’s a 50-50 state, shouldn’t we be trying to find a map that would reflect that in our representation? One of the attorneys in the case actually used the analogy, “a drunken monkey can eventually type Hamlet.” There’s this kind of old saw about how randomly typing, you’ll eventually type Hamlet. But why should we outsource our redistricting to a drunken monkey? I thought that was right on the nose. And so the question that was put to the court was: if you can select a plan that’s more proportional without any cost to all the other principles, then shouldn’t you do that?

LEVITT: The plan that was being proposed was a Republican plan. In terms of outlier analysis, how skewed was the plan?

DUCHIN: It wasn’t skewed at all. It was right in the middle of the distribution. And actually, great story — a piano teacher named Amanda Holt drew these plans with a high priority on keeping cities whole and not using any partisan data. And I totally take her at her word that she did that because if you stack those up against the bell curve of a random sample, they fall right where the meat of the distribution is, so they look just as though they were made without partisan data. And because the political geography confers an advantage to Republicans, the legislature decided it was strategic to take one of Holt’s actual plans, tweak it a little, and use it as theirs. I thought that was pretty crafty PR, just to say, “This is just an enterprising local piano teacher who drew this plan. There’s no gerrymandering here.”

LEVITT: My sense is that before you brought your mathematical approach, a lot of the discussion around gerrymandering was based on visual appearance of the districts. Crazy looking districts, like “Goofy kicking Donald Duck” — which I thought when I heard about it was just someone being pejorative, but then I actually looked it up on Google. That district really does look like Goofy kicking Donald Duck. It’s so crazy. 

DUCHIN: Yeah, that’s a classic crazy-looking district. It’s Pennsylvania’s 7th. If you look at the district, you can not only see, like, Goofy’s ears, an outstretched foot. You remember how districts have to be connected? They can’t be multiple pieces. This particular district was so barely connected, at one place it was connected just by the width of a hospital, and in another place, a seafood restaurant. You can’t make this up.

LEVITT: But what your models have made really clear is that districting plans that look reasonable can still be completely unfair, right?

DUCHIN: Absolutely. Yeah, I think that was another lesson for me, because initially I thought, “Oh, if we can just restrict the shapes to not be so wild, then at least you won’t have as much room to gerrymander.” But over and over again, I’ve seen that when a legislature’s under pressure to make their districts look nice, they can gerrymander just as much. The shapes just don’t turn out to be as constraining as I expected when I got started.

LEVITT: So it’s my impression that you’ve limited your role thus far to evaluating redistricting plans that have been proposed. But it seems like there’s a real business opportunity for you to be the one who designs the redistricting plans in the first place. And I could imagine a sliding scale price wise. So you might charge, say, $500,000 to come up with a plan that was totally fair. But if the majority party in a state wants a plan that’s heavily skewed in their favor, but looks fair and reasonable, maybe you’d charge them $5,000,000 instead of $500,000. And I suspect you’d have a lot of customers willing to pay you the $5,000,000. So have you thought about that?

DUCHIN: I love that you’re setting up my next business venture. Yeah, well, actually, I have been involved in helping line drawers. I just want to say that first, because litigation is supposed to be the guardrail after something untoward has occurred. But I’ve tried to make myself available for independent commissions and even for legislatures. And so, for instance, in Michigan, there’s a new independent commission and the Department of State brought in my lab to help them collect communities of interest testimony from around the state and turn that into something that the commission could take into account. In Arizona, there’s an independent commission and in their guidelines, plans are required to strive for competitiveness. And so they brought us in to help advise them on what would be best practices for trying to design a competitive plan. That’s work that I really like. I like thinking about not just the math to catch you when you’re doing something wrong, but I like thinking about the better processes and process design for doing something right. I also have given some thought to what a good rule might look like. I was one of the people contributing ideas to the partisan gerrymandering language in what became the Freedom to Vote Act. That was this large bill with a lot of different election-related provisions. And one of them was a rule for partisan gerrymandering, a test. This test could help you think about when you’re doing a good job, not just flag the worst. And I have a published paper since that with Gabe Schoenbach where we explore this, and the question was: could you hope to redistrict for some positive goal like proportionality? Or some political scientists favor the efficiency gap or other kinds of standards that tell you what it looks like to do a good job in terms of partisan balance. And what Gabe and I found was pretty interesting. In most states that we looked at, if you take a random sample of plans and you draw them blind or neutral, you can actually find within that sample a number of plans that hit the benchmark of proportionality enough of the time. So the standard in the Freedom to Vote Act is: let’s just look at the two most recent presidential elections, the two most recent Senate elections, so that’s four elections, and let’s see what would happen if you tried to be close to proportional three out of four times. Let’s take that as a test. And to my pleasant surprise, we found that even in the states that are hotspots for gerrymandering — North Carolina, Wisconsin, Pennsylvania — an adequate supply of blindly drawn plans were passing this test. There’s a cool project that came out a few years ago from FiveThirtyEight, which was called the “Atlas of Redistricting,” where Dave Wasserman, who’s a pundit who thinks about politics, and in particular things about gerrymandering — he had hand drawn plans in every state — God bless Dave Wasserman — which tried to be Democratic gerrymanders, tried to be Republican gerrymanders, and tried to be as proportional as possible. He had different alternatives for different goals. And so we looked at his plans and asked: would they pass this test? And he did a great job. All of this to say, you’d like to design a process where it’s possible for people to pass the test without, like, sophisticated consultants. You want a citizen’s redistricting commission that spent some time training and learning how everything works to be able to draw a good plan. And what we found was all kinds of evidence that if you draw a plan that does a good job at being proportional on past elections, it’s probably going to keep doing a good job being proportional on future elections. So I thought that was really encouraging.

LEVITT: One change in process would be to move to a different voting system. Do you have views on what voting system makes the most sense these days?

DUCHIN: Do I have views? I always have views. There are all kinds of reasons to say, even amidst good news, that it’s possible to do a better job with our redistricting. We should also consider doing less redistricting. And one reason is that the direction that courts are going in is pretty clear — that the careful design of districts, especially if you’re trying to design for sort of racial fairness goals, is more and more frowned on. You shouldn’t be doing kind of race-conscious anything by the lights of this Supreme Court, even if it’s to remediate past racial discrimination. And one thing that these methods of constructing all these districting plans that we’ve been talking about has made clear is that while blind redistricting may be bad for Democrats, on average, just based on where people live, it’s devastating for racial and language minorities around the country. The actual spatial distribution is such that you’d be shutting out a lot of groups of the opportunity to elect candidates of choice. And so when you see that, you start to think, maybe this system coupled with the preference for drawing blind, maybe this system is a problem. And I’ve spent a bunch of time in the last few years building up math modeling techniques to compare systems. So for instance, to hold the preferences constant and change the voting rule — so maybe change from party list to first past the post to some kind of ranked choice — and see how the outcomes would be different. For instance, I teamed up with an advocacy group called New America to do a study recently of the Massachusetts legislature, because as we heard, Massachusetts geography is just really bad for Republicans. And so would a different kind of system help? And what we find in that study is really clear — obviously, if you moved to party list, that would take you to proportionality right away, because that’s how it’s constructed. But it also seems like a well-designed ranked choice system gets you there as well.

LEVITT: Okay, so explain. What is a well-designed rank choice system?

DUCHIN: Well, in the first place, ranked choice is just about the question you ask voters. And you don’t just ask voters to pick their favorite or to pick several, but you ask them to rank the choices.

LEVITT: My intuition is that rank choice only matters when there’s a whole bunch of different options, but in a world when there’s a Democratic candidate and a Republican candidate, does rank choice matter?

DUCHIN: So usually it’s coupled with something else that curates the choices. For instance, what Alaska does is a final four system where there’s a kind of first round of voting that’s used to pick the four people who will be in contention when you rank. I alluded a minute ago to a well-designed rank choice system, and here’s part of what I mean by that. You have to design how to curate that final menu of options. And it can lead to wildness. For instance, there was a mayoral race in Minneapolis in 2013 that was done by ranked choice where there were 35 named candidates on the ballot just for one office, which was mayor. And one of the candidates was Captain Jack Sparrow. And generally it seems like a better design is to have some kind of preliminary round that gives you a more limited menu for people to rank on the final round. There’s another thing that people don’t often necessarily think about when they hear about ranked choice. And that is: are you going to use rankings to elect just one office? Or, if you’re trying to fill a body like a legislature, maybe you’ll have multi-member districts — or city council, maybe you’ll have districts that elect several. So a really interesting case is Portland, Oregon, where they just reformed the city council election system to create four districts electing three members each to make 12 on the city council. And my modeling says that that is an especially effective system. When you have the possibility of electing several out of the same district, then it’s easier to get to proportionality within the district. That makes great sense. When you’re just electing one person, you can’t get a fraction of the one.

LEVITT: So that’s interesting. So if you were a dictator or God, you would move to these multi-member districts. Makes a lot of sense. It’s just something that the founding fathers didn’t think about, I think.

DUCHIN: Yeah, these multi-member systems, again, when you’re trying to fill a representative body, they give you a big head start, a big leg up, getting towards proportional representation, if that’s your goal. 

LEVITT: You and I, we have something in common that you would never be able to guess.

DUCHIN: Okay.

LEVITT: It is that Rush Limbaugh, the conservative radio commentator, has ridiculed both of us on his show. Do you want to tell the story of him making fun of you first, and then I’ll tell you the story of how he made fun of me?

DUCHIN: Oh, absolutely. So I was a grad student at U Chicago back in the day, I graduated in ‘05, so this must have been about ‘03 — 2003, something like that. And some students on campus wanted gender neutral bathrooms. And of course, we’re probably all familiar with the bathroom wars that came around 10 years after that. Today I hear there’s a trans representative from Delaware, I think, Sarah McBride, who just got elected to the House, and folks are trying to make it hard for her to use the bathroom.

LEVITT: They succeeded. I loved her response, though, which was — I’m paraphrasing — she said, “Fine. I’m not here to fight about bathrooms. I’m here to make good policy,” which I just thought was a really powerful response to the — I’ll use the word lunacy, it’ll probably make people angry — but the lunacy that our Congress is spending its time saying who can use the bathroom in Congress because they feel threatened. It’s just — it’s so bizarre. Okay, but go ahead. I didn’t mean to distract

DUCHIN: Well, so just to say there were some students who thought it was important to just have an option for some bathrooms that weren’t regulated by sex. I had done some organizing as an undergrad and they just asked me for some advice about strategies to get the administration to cooperate. And we debated it and then we had some meetings with administrators, and to our amazement the administrators were like, “Sure. How many and where?” It was such a non-issue. But The Chicago Sun Times got a hold of it, and a reporter called me and asked if I had any comment. And, you know, again, this is 10 years before this bathroom contestation was a little bit more of a national political issue. And I just said, “Yeah, it was just no big deal in the end. It was something that some students thought was important and the administration did the thing and so now there’s just more choices for people.” And The Sun Times ran that quote — just, “More choices for people,” I think was the quote. And I think this was before radio trollery was quite the art form it became later, but Rush Limbaugh existed and picked up on that and did a long riff on it on his radio show. Also, this was the week he came back from rehab for prescription meds. And so his audience was, like, huge that week. I didn’t know about it, but somebody sent me an email, and was like, “You might want to check out this clip.” So I looked it up. And sure enough, he just goes to town on queers and feminists and all of his favorite people and their ringleader, Moon Dookin. The guy was magic, I have to say. So he goes on at some point that the University of Chicago should line the paths of campus with buckets for idiots like Moon Dookin who don’t know what bathrooms are for. Yeah, I thought that was a good one. And then at the end of the clip, he says, “Goodnight, Moon.” It was like — it was just, mwah, chef’s kiss, just beautiful. That’s my Rush Limbaugh story. What’s yours?

LEVITT: Okay, so my Rush Limbaugh story is from a long time ago, back in — I think around 1995. And I never actually heard the show myself, so I was only told about it by people who had heard the show. So I might not get all the details exactly right, but here’s the gist of it. Shortly after I got my Ph.D., I had written a paper that used the impact of ACLU prison overcrowding litigation to try to estimate a causal impact of a state’s prison population, the size of a state’s prison population, on crime rates. And the details aren’t important, but a magazine wrote about my findings and with a headline that simply said, “Prisons Reduce Crime.” So on his show, Rush Limbaugh says something like, “So there’s this real genius economist at Harvard and he’s come up with this brilliant new insight. Something that no one has ever realized before. He’s figured out that when you lock up more criminals in prison, crime actually goes down. Now imagine that. Wow, what a surprise.” And like you’re saying, he really is magic. He says, “So I’ve heard he’s working on a new research paper now, and the working title is, ‘Nighttime Causes Darkness.’” So I have to say, even though he was making fun of me, as a young academic, I was really excited to be noticed. And it sounds like you’re the same way. We’re both talking like he was trying to make fun of us, but we both are wearing it like a badge of honor.

DUCHIN: Well, I had richly mixed feelings at the time. But I want to say, if you ever come back around and want to prove that nighttime causes darkness, you have a collaborator in me.

LEVITT: I love that.

You’re listening to People I (Mostly) Admire with Steve Levitt and his conversation with Moon Duchin. After the break:

LEVITT: Let me ask you a question, which is probably going to sound blasphemous, but it comes from a good place. 

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Moon was a double major at Harvard in math and women’s studies, and she taught women’s studies courses while she was doing her math Ph.D. at the University of Chicago. I was curious if her training in math informs her thinking on social issues, or maybe vice versa?

DUCHIN: Well, I have a broader interest in what’s sometimes called S.T.S., Science Technology and Society, or Science and Technology Studies, which looks at what we do as scientists and asks about power relations and social relations that inform it. So when I was in college, I thought I was going to do math and philosophy, but I took a first philosophy class and it involved a lot of thought experiments with brains and vats and so on. It wasn’t really about social relations in any way. So I actually came to women’s studies that way, as a way to think about what science does while talking about people. That’s an interest that’s really come through my whole career. I would say the magic of this turn to think about democracy and elections is that it’s really brought that interest in people power and science kind of right into the mainstream of my research program in a way that I, as a pure mathematician, continue to think is extraordinarily lucky.

LEVITT: Let me ask you a question, which is probably going to sound blasphemous, but it comes from a good place. And I think it’s related to what we just talked about. So there’s an active effort to have more diversity among academic economists, more people of color, more women. And I’m sure there’s even more of that in math than there is in economics. And when you first hear about it, it seems like it’s hard to argue with. But I wonder whether at some level it might not be a good idea in the following sense. If someone has the talent to be a top academic mathematician or economist, they have the talent to do a lot of things. And young people are impressionable. So if I find a young person and I take them under my wing and I say, “Hey, you should really be an academic economist,” they might do it just because they trust me. But I wonder whether socially or personally being an academic economist or being an academic mathematician is actually maybe the best life or the biggest impact. And so whether in some sense we might be doing more harm than good. Do you have any thoughts on that?

DUCHIN: Okay, let’s unpack that a little. One piece is just about the question: is it rational to go to graduate school in the first place? I have the great fortune to work with a lot of really talented students of all ages, really, but in particular college students. And I definitely do try to do a gut check that asks, “Are you sure you want to go to grad school? Here’s what it’s like. Let’s talk about what it’s like and what comes next and the trade offs.” So I’m very sensitive to that. But why do I want to be a professor? After all, when I started doing some of this redistricting work and I realized that I could be useful in these court cases, I considered leaving academia and doing other kinds of work. Think tanky work, consulting work. Certainly wouldn’t be giving up on life’s comforts to do those other things. But actually, I love this work as a professor. I love the gig. And it’s partly because I really am an educator in addition to a researcher, and I love the opportunity to work with students. So ultimately, for talented, motivated students, I still think there’s a lot to be sad about the professor gig.

LEVITT: So you’re the winner, right? You succeeded. So many people with so much talent enter grad school and don’t win the academic lottery.  

DUCHIN: Well, there’s other forces at work though that you have to really think about to take your initial question about, “should we push for diversity in academia?” seriously. I’ll tell you one thing that I’ve noticed now. I do a fair amount of not only hiring and admissions, like we all do, but also I sit on prize committees and other kinds of things. And if you’re sitting on some committee that’s giving out some prestigious something or other, there are probably some people on the committee who are, you might say, diversity minded and want to be sure that in contention for the thing you’re giving out, the list includes names of women, people of color, people from whatever kind of marginalized identities. You want to be sure they’re on the table. And then there’s other folks on the committee who have a really pressing concern that, you know, what about the white guys? And you get this really unhealthy dynamic around hiring. And so something I’ve thought a lot about — it sounds like you have too — is how to structure practices around admissions and hiring in ways that get past this kind of team play, and get you back to something that gives folks an opportunity to get to the top of the list and not just be tokenized.

LEVITT: I actually approach the problem somewhat differently, which is that, socially there’s obvious benefit in bringing diversity into academics, but there’s also obvious benefit in bringing diversity into all sorts of other elite areas of society. And I wonder whether for the individuals involved who we’re trying to push and nudge in these different directions, whether we might actually be doing them a disservice when indeed the whole world is open to them. And because as academics, you and I get first pass at them, we have more sway over what they do than, say, someone in the U.S. Senate or in the cabinet. If they got a hold of this person and say, “Look, we need great people like you in politics, you should follow politics,” but we co-opt them before they get a chance to do that.

DUCHIN: Well maybe. I’ve really noticed in the last five years or so — so we have this Covid pandemic, obviously, also a big tech boom that happened before and has maybe tightened up a little bit afterwards. But I find it less and less true that undergrads want to be us in the first place. I think that’s been a little bit of a change. But for another thing, wouldn’t it be patronizing to say to people, “Yes, you think you want to be a professor, but I think you’d make a really great journalist. You’ll have a better life, trust me.” You were talking about trying to get the best people and I think that we need to strive for processes that are fair and that evaluate people based on what they have to offer in the job. And since we’re far from doing that, there’s also room to work on our processes, in addition to helping people become better informed about their options.

LEVITT: Okay, I’m going to ask you the last question. So you’re a theoretical mathematician who, because of your applied work, has gotten to see the real world in action. And at least for me, when I wrote Freakonomics and I got a taste of the real world, I was really poisoned to academics after that because I found the real world to be much more fun. Has your exposure to the real world tainted you on academics like it did me?

DUCHIN: I don’t think so, no. It’s still the case that I step onto a college campus and I see the posters for the talks that are coming up and I get all excited. I really love the life of a campus, and all of the different kinds of intellectual projects that people bring into collision with each other. I legitimately find it tremendously exciting, nerdy as that is.

At a point in time when politics is so divisive, it’s really heartening to me that someone as thoughtful and insightful as Moon Duchin has actually been welcomed into the redistricting process, which is about the most divisive issue there is. If you want to learn more about Moon Duchin’s work on redistricting, check out the website for her center, the URL is MGGG.org. That’s MGGG.org.

LEVITT: This is the point in the show where my producer Morgan joins me and we tackle a listener question.

LEVEY: Hi Steve! So, a few weeks ago we had Richard Reeves on the show. He runs the American Institute for Boys and Men. And you and he really dug into why the current education system isn’t working so well for boys. And at the end of the show, you asked listeners to write in with new and radical ideas for overhauling the education system, which is not a new topic for the show, but one we like to revisit often. We got a lot of emails from listeners, didn’t we?

LEVITT: We sure did. And I have to say, this was the single most thoughtful set of responses we’ve ever gotten to a request for our listener ideas. I found myself nodding in agreement with almost every suggestion. Did you have the same reaction?

LEVEY: Yeah, we had a lot of great emails and people from a range of backgrounds — some former educators, some people involved in running schools, a lot of just parents who have witnessed things with their own kids. Do you have, maybe, your top five favorites?

LEVITT: Yeah, I liked a lot of the ideas, from kids spending one school week per year in nature, to banning homework, to having older students spending a big chunk of their time teaching younger students. Many listeners would like to see higher salaries for teachers, which makes sense to me. Being a teacher is an important job, and it’s a hard job, and it’s a profession where there’s a huge gap between the people who do it well and the people who don’t. And in particular, I’d love to see really substantial merit pay for great teachers, although I’m realistic about the practical difficulties of doing that well, especially in a system where teachers are unionized. But my single favorite idea, mentioned by a long-term educator named David, is to get rid of grades and replace them with a mastery-based transcript. I obviously understand the logic of why we have grades, both to provide incentives to kids and to help college admissions decisions, but my own opinion is that grades have become toxic. When you give people strong incentives, like grades, they respond strongly. And I think grades have become such an obsession among students that they now interfere with real learning rather than encouraging it.

LEVEY: So the mastery model is one we’ve talked about on the show before, particularly with Sal Khan, the founder of Khan Academy, who’s been on the show a few different times. Can you just summarize the mastery model?

LEVITT: Yeah, the idea is that students tackle a topic and they work on it as long as it takes them to actually understand it. So if they can do it in a day, no problem. If it takes them two months, that’s fine too. It’s not like you take a test and if you fail the test, you’re done. You take a test and if you didn’t get it, well, then you can keep on working at it until you get it. In some ways, it’s more informative for a college because it actually tells you what the child has really learned. In other ways, it’s less informative because, in the end, most of the kids will end up mastering everything, which actually, is the goal. It just makes it harder to say who’s ahead or behind in the way we typically use grades.

LEVEY: Another idea that listeners had that could happen with the adoption of a mastery model is — grade levels aren’t associated with age. Would that play a factor where students of all different ages might be taking classes together based on how long it’s taking them to grasp a particular concept?

LEVITT: Yeah, absolutely. And there’s a great example from a gentleman named Terry, who’s from Canada, and he’s a principal. He’s got kids who play hockey. And when you show up for the first couple of days of hockey practice, he said there are eight adults with clipboards in the stands making detailed comments about each kid’s talent level, and then assigning the kids appropriately to what team they should be on. And he contrasted that with what he does as a principal, which is to just take kids and arrange them by age into a classroom, where they’re all taught the same thing, regardless of whether they need it or not. It probably tells you something about the importance of hockey relative to education in the Canadian mindset, but it’s a really good, funny, but compelling point that it makes no sense to have a teacher stand up and teach 30 kids the exact same thing when those 30 kids are at all different levels.

LEVEY: And the only thing that’s linking them is age.

LEVITT: Exactly.

LEVEY: In this new mastery school environment, are kids graduating high school at radically different ages?

LEVITT: Typically, the view is still that students will stick around in high school for the same number of years, but the more advanced students will likely do a bunch of community college or university level courses while they’re in high school. People have the view that it’s not a great idea for 14 and 15 year olds to be wandering around college campuses as college freshmen. It’s better to keep them closer to home in the short run, and let them do the coursework, but not have the full independence until they’re, say, 18 or 19 years old.

LEVEY: So you really like this idea of getting rid of grades. Doesn’t that present a pretty big issue for colleges who are evaluating students for admittance?

LEVITT: So it’s not like the college will have nothing. They’ll have a list of all the topics you’ve mastered, so they’ll know a lot about you. But my hope is that colleges will actually be forced to look for more important traits that students have, like curiosity or true enthusiasm for learning. And if I had my dream, what students would leave high school with wouldn’t be a transcript. It would be more like a portfolio where the student could show, “Hey, here’s all the things that I learned, all the topics I went out on my own and I delved into. Here’s the business I started. Here’s the volunteer work that I didn’t just pretend to do because it would get me into college. But here’s what I actually did.” If grades disappeared and colleges were forced to evaluate students on real traits, I think we’d have students who are incentivized to do things that matter, instead of just grinding for grades.

LEVEY: Okay, but isn’t it going to take colleges and universities now 20 times longer to evaluate an individual student?

LEVITT: If it did, I wouldn’t exactly cry for the colleges. If they’re not concerned about getting the best students, they can just draw names out of a hat. It seems like they should be willing to put in the effort to try to find the best students.

LEVEY: Thank you to everyone who wrote in. If you have a question for us, our email is PIMA@freakonomics. com. It’s P-I-M-A@freakonomics. com. If you have a question for Moon Duchin, we can try to bring her that question and get it answered in a future listener question segment. We read every email that’s sent and we look forward to reading yours.

Next week we’re back with an encore presentation with Harvard psychologist Dan Gilbert, this turned out to be one of the most popular episodes we’ve ever done. And in two weeks we have a brand new episode with historian Elsa Richardson, whose recent work is all about the history of the human gut. Don’t want to miss that. As always, thanks for listening and we’ll see you back soon.

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People I (Mostly) Admire is part of the Freakonomics Radio Network, which also includes Freakonomics Radio, No Stupid Questions, and The Economics of Everyday Things. All our shows are produced by Stitcher and Renbud Radio. This episode was produced by Morgan Levey with help from Lyric Bowditch, and mixed by Jason Gambrell. We had research assistance from Daniel Moritz-Rabson. Our theme music was composed by Luis Guerra. We can be reached at pima@freakonomics.com, that’s P-I-M-A@freakonomics.com. Thanks for listening.

LEVITT: I think I would have taken more math classes if you had been my professor.

DUCHIN: Life is long. We have time.