Math the vote pt I: The geometry of gerrymandering

Gerrymandering has been described as the process by which the people being elected get to chose the people that elect them. It turns out that, while many people would argue that gerrymandering is not healthy for democracy, doing it right requires some maths.

Dr. Thomas Weighill is a mathematician “weighing in” to do just that. At the time of recording, Thomas was at the MGGG (Metric Geometry and Gerrymandering Group), at Tufts University, where they use computational geometry and topology to study gerrymandering. In addition to their academic work MGGG has partnered with civil rights organizations to protect voting rights. Learn more about Thomas, his work, and why he's nicknamed the Pennsylvania postdoc! Follow the work of MGGG on twitter @gerrymandr.

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Thomas has since moved on to begin work at University of North Carolina at Greensboro, but you can keep up with his work on his website. The featured track for this episode comes thanks to Nicholas Burgess, and while the title “I’m scared” seems a little on the nose, we’re still rocking out to it! You can find more of Nicholas’ work on bandcamp and we are so grateful that it was made readily available through creative commons!

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You can find our full length conversation with Thomas on YouTube. Subscribe now if you like your Scicomm on the longer side with fewer edits.

Episode transcript

[Background intro music playing is "I'm Scared" by Nicholas Burgess]

Parmvir: Hello 2scientists friends, we're back with season eight and we're so glad you're tuning in. It's been a long time since we've released an episode, but we spoke to Thomas Whitehill just before the 2020 elections about math and gerrymandering. And it seems like this one continues to  relevant so let's just dive into math the vote part one, the geometry of gerrymandering

[Music fades out]

To our, two audience members. Thank you for showing up. If you haven't been to one of our 2scientists podcasts before, my name is Parmvir and I am the host. David usually hides in the background taking pictures somewhere and yeah, it's been a while since we recorded anything because pandemic and we've been tired, we're pretty sure everybody else has been tired.

And in the meanwhile we are in the midst of I don't even know how to describe the current US selections. Other than anxiety inducing. And so we thought we'd distract ourselves by talking more about elections? And so our guest today is Thomas Weighill. How are you doing

Thomas: Yeah, I'm doing all right.

Thanks. Yeah.

Parmvir: So do you have like a kind of like a pandemic? What's the word I'm thinking of, some kind of defense mechanism of choice. So I just started running again recently.

Thomas: Yeah. I think that'll be it for me. I started jogging, although I'm not sure you can call what I do jogging. It's, it's sort of about the length of about three of my favorite songs.

But that has really helped, my sort of internal anxiety gets soothed by the notion that I can't possibly be sick if I can run x amount of distance every day which I'm sure is hopelessly flawed, but that's, I would, I try to go for a run most mornings and in general, it's that, and I've completely switched to whole foods.

From that, you know, I used to go to like the proper, we have this place called market basket, which is a traditional awesome place to buy everything you could ever want. And I'm ashamed to say, since the pandemic started now, I'm like purely buying from whole foods. So I'm getting all kinds of, I'm eating a lot of kale salads and things, but no, each to their own,

Parmvir: I guess.

I mean, I think we're getting more takeout than ever before, but like I say, coping mechanisms. So the, the point of today's podcast is to talk to you about kind of how you got into math specifically where you studied. And a little about your research. So tell us your kind of mathematician origin story.

Thomas: Sure. Yeah. I've, I've worn a couple of different hats in sort of, I guess, STEM fields over my life. So I guess my exposure to math that's fun, as opposed to math you have to do it goes back to when I was in South Africa, growing up, I got exposed to the math Olympiad training stuff. So I think this is a thing sort of throughout the world where you know that from sort of high school ages, folks get together and you practice on these kind of fun math problems.

So it's not like adding big numbers or solving a quadratic equation. That's cool stuff. Like, you know, if I draw these triangles in these circles, what happens and eventually you sort of progressed through the ranks and if you get selected, you can go to the international math Olympiad, which is a big deal.

Like a lot of extremely famous mathematicians got their start there. My advisor was a gold medalist at IMO in the states. Yeah, so I kind of got exposed to math there and I went on math camps which was extremely nerdy. I have the t-shirts to prove it. Absolutely adored that. And then I immediately went to do engineering at college in South Africa.

And essentially because I didn't think I knew that a mathematician existed, like, I didn't know that you could just do math as a living. That math was kind of a thing that you could use to make money by building bridges or building robots or whatever. And I, I enjoyed my time studying engineering, but this was at a place called Stellenbosch University.

So I consider it to be a very good engineering degree. Had a lot of fun. Realized I was much worse at all the non math stuff than I want it to be. I was sort of, it was, I would sort of do okay. Calculating everything out. And then if you put a soldering iron in my hands, you just needed to get well away from me cause something bad was going to happen.

And so that was kind of what I was doing officially. During that time I met someone who would eventually be my master's advisor. He was sort of mathematician and category theory. And I think that like if you talk to mathematicians sort of professional math folks, they there's like a common denominator, in their stories that there's someone who grabbed them at some point in their career and convinced them that math was like their calling and like really showed them.

Math is, math is not advanced calculus. It's not just doing bigger integrals. It's this amazing exploratory thing that you can live in and that you can just... It's so this thrill that you get, and for me, that was my master's advisor, a guy by the name of Janelidze originally from Georgia the country, not the state.

And yeah, and so I sort of taking classes with him as did my wife the only math class I ever took with my wife she promptly got much better grades than me, but nonetheless, he thought that I was good enough. And then I kind of had a decision point at the end of my undergrad to either carry on to doing engineering things, to do some kind of like, it was weird, some kind of cross disciplinary data stuff, or to do math.

And I decided to take the funding of the second one and combine it with the actual research of the third. So I managed to convince essentially, a media company to fund me to do category theory, which is abstract math. It's so abstract that abstract mathematicians are like, no, no, come on. Really. I sold them on this idea and yeah, I'm happy to sort of chat about that environment, but it was not good for mathematics, but it was free coffee and foosball tables.

It looked like the inside of Facebook. They had clearly decided they wanted to build this kind of crazy looking lab. So I did a master's thesis in this sort of really abstract realm gesturing at some applications to real world stuff. And then I came to the US to Tennessee to do my PhD. And again, I kind of had a couple of options.

I was exploring sort of more applied stuff, having sort of downloaded abstracts. I ended up settling on doing a PhD in basically geometric topology. So studying spaces, again, like really abstract, like not stuff that you would want to sort of talk about over the dinner table and say, well, this is helping us fight wildfires or something.

But I loved it. I thought it was great. I had a lot of fun doing that. And then when it came time sort of end the PhD, I looked around, went on the job market. Anyone will tell you that's a soul crushing experience in academic mathematics. You know, sort of the cost we pay for having the best job in the world is that there's not that many positions out there.

But one of the sort of most attractive options was with Moon Duchin, my current supervisor, my current PI at Tufts university. And I'd met her twice before at conferences and kind of, really been blown away by sort of her career track and what she's been doing. So she has been extremely well-respected in her sort of pure math field, but then she kind of made this pivot into thinking about gerrymandering, redistricting voting rights and sort of completely revolutionizing the mathematical theory in that area.

And I thought like it was, I mean, to me it wouldn't have been as surprising or appealing if someone from say statistics or calc sort of some analysis people had been doing this because that's kind of a natural modeling progression, someone who was doing what I was doing, which was geometry and topology to make that change that really caught my eye.

So I applied and I got the position. I started my postdoc last year in July, and I very, very, very quickly learned a lot about redistricting and gerrymandering. Cause I was very invested in the topic, but I didn't know much to start with. And that brings us pretty much up to today where right now I consider myself someone who does geometry anthropology and I've, I'm still trying to get papers published, which are just pure mathematical imagination, abstract stuff.

But I spend a lot of my time thinking about how topology and geometry well you know, kind of inform the way we think about data and you know, if you're going to do data science, you should have a pet, you should have some interests that motivates you. And right now that is redistricting and elections basically.

Yeah, so that's a long walk from high school.

Parmvir: Oh, it's great.

Yeah. It's a great foundation because actually I was going to ask you a bunch of these questions. So you you're one step ahead of them. But one of the things I'd like to ask is, obviously since we're talking about the subject of gerrymandering and neither of us are originally from the US, and this was a very foreign concept to me when I moved here, I'm sure there's some version of redistricting elsewhere, but can you explain what it is?

And actually if you know, if it occurs in other countries?

Thomas: Yeah, that's a good question. So just to frame it so the US in particular, but some other places elect people to governance by drawing, by taking your geographic regions. So if I'm Pennsylvania, I want to elect 18 Congress people, and you draw some lines and you divide it up into 18 districts.

Each of those 18 districts sends one person to Congress. And gerrymandering is sort of the fact that or the sort of technique, whereby you realize that, you know, who draws those lines matters a lot. So, you know, you can think about some examples of this, but basically it turns out that where, how you draw those 18 districts can make a difference on any given day as to like who gets elected and how, what kind of party affiliation they have.

Right. So it turns out that it's this sort of obstruction. I'd like to think of it from people expressing their will, right? Like folks are going to the ballot box, just want to vote for someone who represents their interest. But if they're, if people are messing with the way you can vote, then you, then you're sort of disempowered from being able to.

 I'll be honest. I'm not an expert on gerrymandering in a lot of other countries. Where I come from in South Africa, we have party list proportional representation. So that means you go to the, in this country, that would be, you go down you, write Democrat or Republican, then you walk out. And then the Democrats and Republicans fill the Congress with whoever they want. And you know, the debates between that and districted systems is so old and belongs to so many people that aren't me, that I won't try and sort of state anything affirmative. I'll just say that, you know, that the standard arguments against it, for that with districts, you know who your representative is, right?

Like we can all phone, our Congress people, we can get them on the phone and talk to them. Whereas if you're voting for a party, well, you know, unless you happen to know the chairman of the party, you might not be able to access the person that you elected. But on the other hand, we just spoke about gerrymandering, of course, with proportional representation, the party lists you eliminate that completely.

Britain has a bit of a history with this. Like some of the earliest anti gerrymandering stuff was to do with the fact that there weren't population bounds on what you could draw. So Britain would do things like draw a a little parliamentary region which had three sheep and two people and the left someone and send them off [Parmvir laughs].

You know there, there is a skit in Black Adder, which does always makes me think of, but I realized  this TV show is not as well known in this country, so I don't employ it as often.

Parmvir: I think it's on Netflix, so I think people should go and watch it.

Thomas: Oh great. So I think it's whichever, I think it's the Regency Black Adder, three, I think. Yeah. And, and in other countries what's more common is either this kind of proportional representation or you have sort of, I guess like multi-member districts sometimes.

So you have a district with more folks being elected and that tends to like ameliorate some of the issues. If there's more people being elected from each district, you have a better shot at like something like proportional representation. And in my very limited experience, you tend to get more proportional results with that.

Again, I'm kind of treading on, on ground that really belongs to political scientists and sort of whom I'm very happy to collaborate with, but I don't pretend to be one. So yeah, that's not perfect answer, but yes.

Parmvir: So do you know what the inspiration behind the group was?

Thomas: Yeah. So Moon kind of got dragged, not dragged in, willingly dragged into the whole thing by a good friend of hers who basically convinced her that mathematicians needed to weigh in on this issue because at the time, at the time, very little was understood about this issue.

Folks had been drawing lines for ages, but we hadn't reached the stage when data and computation had caught up to the point that you could say concrete things about it. Like you could look at a map that someone had drawn on, like literally by hand and say things about it. You know, no one was going to be able to use a computer to sort of simulate stuff based on it.

And the original focus, I think all of her work was to do with district shape. I mean, this is an issue that at some point we're going to discuss, because this comes up in gerrymandering. So I might as well say it now, a lot of folks think of gerrymandering as ugly districts. Districts that look terrible. So these windy things, like anyone from Maryland knows their district looks this terrible snaky thing, Pennsylvania had a district called Goofy kicking Donald Duck for a while which is a pretty accurate statement.

And it turns out that two things are true. One is that there are reasons to have weirdly shaped districts that have nothing to do with nefarious intent. And two that you can draw lovely looking districts and get exactly as much advantage for your party.

Classic example of this. In Pennsylvania, where there was this Goofy kicking Donald Duck situation and the Republican controlled State Senate, I think, floated a plan on Twitter that looked gorgeous. I think it looks gorgeous. I love it. But if you ran the math, it had exactly the same electoral outcomes as Goofy kicking Donald Duck. And, and so, and this kind of, this was simultaneously a bit of a crushing revelation, I think in the sense that we thought that we would just be able to apply some nice discrete geometry. How much is it curving? How much is it, how weird is it? But it actually blew the door open to this, like, okay, what are we dealing with here? How do we even begin to understand this problem? And Moon sort of like, and I don't envy her for this at all was consulting for Governor Wolf in Pennsylvania during the redistricting mess that happened in Pennsylvania. Realizations like okay. We need to draw some maps. Where is the data and the legislature responding, "well, we won't give it to you". I think they said this in court. "We won't give this to you also. It doesn't exist", and sort of the shock and horror of realizing, wait, hold on. You're telling me we don't know how people voted in Pennsylvania.

Like, no one actually knows those kinds of things. So yeah, basically it started with this idea of, okay, we're just going to measure shapes and it just blew up to be so much more. And then she started this group initiative. This group was kind of like a early Microsoft kind of, couple of kids in a garage kind of situation, doing amazing work. And to this day, I don't understand how they got it done back in those early days. But then sort of, we found a nice home at Tisch college in Tufts university. We were able to actually, you know, hire some people on some kind of decent term basis. And now we're this research group.

I like to think of us as probably the leading research group. Although, I'm probably upsetting some folks. I'm allowed to be biased. It's my research.

Parmvir: Absolutely. So from a very practical point of view for me, this is the kind of math that my brain can compute because once it gets too abstract, it's just like, I have no idea what's going on, but for me, this kind of applied mathematics makes a bit more sense. So how is it that you, what does it look like for you to do your research? Remember I'm a biologist and I do experiments for a living.

Thomas: Experiments. Yeah. We do experiments as well. Our experiments consist of, so we don't do a thousand assays, we do a thousands redistrictings of Pennsylvania. Well, actually we do a million redistrictings of Pennsylvania because computers are awesome.

Yeah, so like our central business is answering questions about redistricting and gerrymandering empirically using computational methods. So what I'm super interested in is, I'm sort of interested in two different things. I'm definitely interested in like, how can we make an impact? Like that is a question that has to be answered. And often you kind of have to put your ego to the side there and realize that the simple intervention you can make is, is the one that will work. Maybe, what you want to do is, you know, apply persistent cohomology modules to this problem. But really what you need to do is just add those two numbers.

And if they're big, there's a problem. Like sometimes you need to, you know, put aside what you'd like to do, but I've found that this area gives rise to tons of unexplored questions that are emblematic of a lot of data questions we have right now. And I, so for me on a day-to-day basis, what I'm trying to do is take the new way of mathematical data science and trying to find ways to both use the exploit that, to solve the problem that we might have, or, you know, to inspire something from that problem.

To give you a sort of a concrete example. I said, we did a million redistricting pans for Pennsylvania. Okay, so you can ask a number of questions about that. But the question was interests me is what does the average one look like? That's, kind of, it's it tends not to be like a fun complicated question, right?

It's not super obvious what you mean by average, right? You draw a bunch of different maps and you know, this may be someone's district in one of those maps, then they changed districts, but the districts don't come with God-given numberings, there's no district 18 because you've just drew a map.

You didn't say where district 18 was. And so you've got to find a clever way of saying what are the what's like the basic central tendencies, right. Can I point to a map and say with some conviction? Yeah. There's usually, there's usually two districts there, one there, one there, and that one's always democratic.

That's that's the kind of insight that I would like to mine from the millions of maps that we generate. And it turns out to be a super fun.

Parmvir: So I was looking on the website and the group is quite big. What are other people doing and how are the, the various ways that people come to approach the problem?

Thomas: Yeah, we're big and we're multidisciplinary. We have data scientists, geographers. We have myself, which I guess is a mathematician slash data scientist. And we have essentially folks who are really into programming and we have people who are just at the intersection of all of that. So we've got a number of projects on the go right now.

And, you know, as usual in a research group, people kind of find things that interest them and we all discuss what's needed on which projects. And we all kind of generally just driven by our interests. But one of our big projects is something called districtr.org which is a website where you can draw maps and this was, sort of, again, developed by someone in the early days initially. Again, a huge lift that I don't know how they did, but now is an active development. So we have two software developers, I think, is what you would essentially call them, plus a geographer working on that sort of every week, adding new features carefully sort of turning and also trying to figure out like, what is the market and I don't, when I say market, we're not making any money off this.

I mean, users, right? Like you won't see an ad for anything anytime soon and district but sort of, how can we bring this to communities? How can we let people play with us in a way that that matters? Our data scientists are, involved in a bunch of different projects right now, we've got a project where we're studying election reform, which is sort of, it's kind of a natural spinoff from our gerrymandering work.

So I just discussed it like you can elect people by district. We connect people proportionately. Another way to do it is to come up with an alternative voting system, like rank choice, which is on the ballot to Massachusetts actually which is sort of a more sophisticated way of electing folks.

And  I'm sure some people have heard of this and, and maybe have strong opinions about it. Our work is about how do you predict when that will be a good option, especially for marginalized communities. And so I think I'm working with one of our data scientists Dara Gold on this project, along with a geographer who used to be with us who's now at grad school named Ruth Buck.

And that's been a very interesting project to consider. That's a classic case where the math is so, it's such a small part of the battle, as any good math modeler knows, it's like, you've got to think very, very hard about the context before you press a button on any computer and just simulate stuff and let it go.

Yeah. So that's some of the stuff that's been going on. We also got I will mention brought into the fight against COVID a little bit too. We're currently also in-house developing the app that Tufts uses to do the testing scheduling. And so this is for COVID on Tufts campus and a few other places as well. And this was basically a case of someone. I think the president of Tufts realized that we were a sort of a treasure trove of geospatial data science skills. And he was like, you know what, I'm gonna put these people on the case. And we all learned a lot of, very, very quickly at the heart, basic epidemiology and queuing theory.

I think it's been pretty successful you know, as a venture. So we get up to a lot of different stuff. Yeah.

Parmvir: So you mentioned earlier that you don't make any money off of your, the site that you were talking about earlier, but David is sitting over there sending you messages. He wanted to know are people like you hired by political parties with the intent to maximize their political fortunes? He says a bit like white hat hackers versus black hat hackers.

Thomas: Well, I'll tell you I haven't had any offers, but you know, my impression is that I don't know. I don't, I think it's possible that there are, and I don't know about it. It's so under the radar, my impression, just from the very couple of things I've seen, cause we do have transcripts of certain things is that the political parties and the line drawers are not quite as, quite where we are in terms of the research, like they're catching up.

I think that they are going to have to adapt pretty quickly to a scenario where we have the ability to scrutinize a lot of what they're doing when they're drawing the lines. Some of the best work that gets done in this area is by expert witnesses. One of the earliest things the MGGG did,  (ee) (that's our group, rolls off the tongue) is went around the country training expert witnesses to talk about fair redistricting, to be able to stand up in court and say, this map is fair, this map is unfair. And why do we believe that? So, you know, I have a tremendous amount of respect for the work those folks do sort of fighting the fight. Right. Cause we write the papers, but we're not, we're not on the front lines. And that we try to support folks like that, but by training or by providing resources.

But I'm not aware of any, any black hat gerrymanders up there. And I can't, people sometimes ask like, can I use, we have an algorithm? Can I use your algorithm to gerrymander? And my general response is no. You really can't, like our algorithm is very good at figuring out what is a typical plan. It's not great at drawing a plan like some specifications, at least not much better than most people are. Like, I don't know. I've seen people on Twitter posts gerrymanders using our district app. Actually they'll sort of say, look at this awful gerrymander of Michigan. So I don't think it's that hard to draw a gerrymander.

Honestly, I think that what's hard is, I mean, the Supreme court has been asking for this decades and eventually just gave up, putting your thumb down and saying, okay, this is, unfair for the following verifiable reasons. That seems that that's the way more challenging question. Then just drawing an awful map which people have been doing since the word gerrymander was invented.

Parmvir: Nice. So we're getting some questions from other folks, but before we get to the one from Mike, I wanted to ask why Pennsylvania seems to be the one that keeps cropping up.

Thomas: There's a joke that I'm the Pennsylvania post-doc to be honest.

So, there are a couple of states that have really been battlegrounds with us. Pennsylvania went through a whole thing where they had, I mean, there's a couple of reasons. So going through them, firstly, obviously Moon was involved, she was in the fray of this whole thing where the proposed plan in 2011 was awful and there were multiple attempts to replace it.

And it was a series of battles between the, I think the league of women voters in Pennsylvania and the, and the people drawing the lines to try and get a fair map for Pennsylvania. And I think they were successful in the end. I think the current plan, which is the so-called remedial plan drawn by a, special master. So this is someone who comes in externally and draws the plan for you, typically a college professor. I think it's a really good map, but this compared to what we've looked at previously, and we have the data to back that up. But my sort of obsession with Pennsylvania, I think comes from the fact that I wrote a book chapter, which is going to come out next year and we've got a book coming out folks it's called political geometry. Birkhäuser Basel is gonna get, they're going to publish it at some point next year. And it's a fantastic book. It's just a sweep of various different academic insights into redistricting. So we have stuff on law, stuff on political science, stuff on math, stuff on sort of on the ground folks who are actually dealing with this.

And in that I wrote a chapter which sort of beat Pennsylvania to death. Data-wise like, I think we looked at every possible election, every election we could find and for the last sort of four years or so, and every single way of drawing districts, from districts which are normal sized, to districts which are like half this like tiny little guy. So I think we went from, what if Pennsylvania had three districts to what if Pennsylvania had 220 and we ran every single number. I've just got pages of like excruciatingly deep dive on every possible perspective on Pennsylvania. So yeah, hotbed of gerrymandering. Really bad data, ironically, despite my obsession with it.

And for some reason it's just a interesting case. I guess another thing to say about Pennsylvania is that it tends to lead to disproportionate outcomes. So Democrats are never quite able to get as many congressional seats. So Pennsylvania is 50, 50 ish. Okay. It's like a purple-y state Democrats in, sort of in the really gerrymandered plans got very, got hammered very badly.

Often the Democrats complain that they can't elect enough Congress people out of Pennsylvania. And what's interesting is that if you sort of run the algorithm and you run the numbers that Democrats shouldn't do as bad as the, as the worst gerrymanders out there, but they're, but even plans drawn by a neutral computer don't tend to award Democrats quite their proportion. So this is a nice little mathematical puzzle. It's a puzzle to think about why is that? Well, you can, you can say some easy things. Like, well, Democrats tend to cluster in cities and this is bad, but you peel away at that and you start to get in sort of to much more complicated territory of, you know, what is it about that that's bad.

So I I've given you like four or five reasons why Pennsylvania, for some reason coming up, if I think of any more, I'll let you know.

Parmvir: They all seem legit so far. But the, so the question from Mike was can we discuss the utilization of math to determine the degree of gerrymandering? So his background included the navigation routines of optimizing lunar, excursions of the lunar excursion module.

Thomas: Okay. That is extremely cool. So, the engineer side of me that cries during Apollo 13 that is very impressed by that. So let me, let me roughly sketch that out quickly. So you've got a map in front of you. The first thing you can figure out is if everyone voted the way they did for Clinton and Trump, who would win and by how much in each district, that's something you can do if the data was there. As we said, it's not always there, but let's suppose we're in a nice state like North Carolina, which has gorgeous data. It's a wonderful. Okay, now you have to decide if it's gerrymandered or not, and you have a number of different choices. One thing you can do is you can try and set up a clever formula for how did the party do.

Without really considering where you are and what's, what's going on in North Carolina specifically. And so there's a couple of these there's efficiency gap. There's partisan symmetry mean median scores. These are all basically ways of looking at the districts and how many people and sort of the vote shares, like how people voted in those districts and making a one-time determination on how like middle of the road fair is it?

You know, and so this has been sort of accepted by a number of places. The courts have sort of been iffy on it. I mean the Supreme court eventually didn't accept anything, but they didn't like this. And the, and all sort of main I guess not objections, but sort of the main criticism against that is that you're really not taking into account the specific case. Right. What if it's the case that the efficiency gap in North Carolina is usually 0.1, no matter how you. But in some other case, it's minus 0.1 or something, you know, and this is not idle talk. We do have a paper which is a little bit of a hot take. It's pretty spicy, but we've checked the math that sort of pokes holes in a lot of these traditional classical ways of just looking at numbers.

So our approach is slightly different. What you do is you say, okay, we know you drew the lines and it seems pretty suss. So what we're going to do is we're going to generate every other way. You could have joined them. And we're going to see how you did compared to that. If you gave, if you managed to give Democrats more seats than every other plan we drew, well, it sounds like you were engineering something there.

So either you got very lucky or something was going on. And so, okay. Where's the math? Well, the hardest question is what about these other plans? How many are there? It's more than the number of atoms in the universe. So you've got a bit of a problem. You can't possibly enumerate them all. And in fact, you don't want to most of them are horrible.

Most of them look terrible. I mean, they make Goofy kicking Donald Duck look beautiful. So you've got to think like, what is a good representative sample of desirable maps to compare against? And that question is, that's what drives, that's what keeps us up at night is even though I think we've got a really good algorithm for it. Like that is the big question is sort of how do you go about doing that? And we're not the only folks doing that by the way. There are other people like Wes Pegden, and Jonathan Mattingly in North Carolina who are also doing this kind of stuff right. Where they generate huge numbers of different plans and they do this stuff.

And so we're not the pioneers. But, you know, we have our special sauce algorithm. Its name is recom stands for recombination. And you know, I think it's, it has the advantage of being something that you can run on your laptop as opposed to something you have to hand to a supercomputer. And so far it's proven very, very useful as a way to detect gerrymanders.

So, and they refer to these as ensemble methods. Ensemble means you've generated the bunch of different plans. And then you look at specifically that one. So yeah, that's our point of view and that's sort of the background as well of what other folks are doing in this space.

Parmvir: So we also have a question from Jack, which is: when you're working with this kind of data, what is the spatial resolution?

You mentioned that you were looking for an "average map'. You saw that some regions always turned up democratic. Is it possible to make a political heat map?

Thomas: Yeah. So that's a really good question. So a political heat map or geographers call them color plates. You can take your state and you can try and look at, you know, where did Democrats vote? Where did Republicans vote? So a state we haven't spoken about a lot is Pennsylvania. So in Pennsylvania, Philadelphia and Erie and Pittsburgh and Scranton, these places are really blue and everyone else is red. Okay. But how do you actually see that? Well, we don't know how each person voted.

Fortunately, the US democratic system is strong enough that we don't have access to that data. All we know is at some level, we know how the votes were collected. Now, if you see a picture of a state and how it's voting on election day, so coming up, you're probably seeing it by counting. You're probably seeing like this county went for Clinton. Well, in this case, Biden and this county went for Trump. But there's a finer grained level you can go to, which is voting precincts. And so if you have actually voted in this country, you probably know what your precinct is. It's kind of like, you know, it might have one polling place might have more, but it's sort of the way that they're going to tabulate your vote, that's the region.

And so one of the best ways to visualize things is just to look at precincts  and color them red and blue, depending on which way they went. And that will give you some kind of political heat map. And if you stare at that for long enough, you can sort of gain some insights from that.

You can try and go lower because districts aren't always drawn out of precincts, which is annoying. Sometimes districts are drawn cutting precincts in half, not all states, some states do. We wish they would all respect precincts but they don't always. And then you've got to make some fun statistical decisions about how do you guess sub precinct vote totals.

And there are a lot of ways to do that and that's sort of a whole field in its own, basically. It's sort of, okay. I know how people voted in this big unit. How did people vote in the smaller units? So you can go lower at some cost.  But what I think is a super interesting question and what motivated some of my research was, you can look at this political heat map of red and blue areas, and then you can draw districts. And when you draw districts it's kind of like, you're almost losing quality in your video. You're like, you know, you're compressing the data because now you've got maybe two blue cities and you put a district right on top of them. Now they're now they're bound together. They're going to vote for the same congressperson.

So the big question is, okay, you've got the political heat map. You can look at that. How does that subtle variation there translate into who wins big districts. And that question's kind of hard to answer it. So when I say something like in the average plan, this district always goes for Democrats is not about looking at the map and finding blue. It's about finding the right size of blue to fit neatly into a district. And that's kind of hard to predict beforehand, but fortunately, you know, if you draw enough maps, you can gain that kind of insight.

Parmvir: Has your research impacted anything about how you see you as politics?

Thomas: Oh, that's a nice one.

That's a good question. It's hard to answer that question a little bit because  my increasing awareness of US politics ran sort of parallel to my involvement in it as a research topic I think. Yeah. I'm trying to think of sort of one pithy insight right.

But I guess something I've sort of realized is that nowhere near as simple and that looking at it in a quantitative way, you often tend to do that. Like, you know, we often simplify things and mathematics too, you know, Democrat or Republican, or we talk about voting rights act and  we sort of look at a district and we say, because the district has a 52% Black population, therefore it's effective for representation for Black voters.

And you know, this is sort of like the, the mathematicians way of looking at things. But if you spend any amount of time staring at the problem and actually talking to folks, you realize how much nuance there is. This comes up a lot in our work on election reform. So we, we like to talk about rank choice voting a lot, and we like to run the numbers and say, rank choice voting does this, and districts would do that. But at the end of the day, nothing about that will change the mind of someone who says, you know what? I like to know where my representative lives. I like them to live on my city block. And I don't care if your math models say that in some abstract sense, we'll get more representation that's my buy-in to democracy. That's how I want things to go. So I guess that's, I guess my main insight would be that we need to be careful of, you can call it a quantitative fetish. We need to be careful of trying to put binaries and numbers on things and ignoring the local context of what's going on.

And that. Absolutely still a place for people to do the hard work of understanding for this very specific community and this specific scenario, you know, what is at play, you know, talking to folks and, getting beyond just surveys and polls results. I'd know, maybe that's a bit of a generic concept, but I think that's a reasonable way to summarize.

Parmvir: Yeah. I mean, people are so, they're just so very complicated. Like, it seems like it would be difficult to try and solve this as a math problem without, without speaking to people as well.

Thomas: Not that there aren't people trying. I think there's a lot of people who are trying to remove the human element from a lot of the stuff we've spoken about today like redistricting. I think for a lot of folks, the answer is if you give a computer enough objective functions and press the optimize button you'll get the perfect map and we can all carry on with our lives. That's not our point of view and it's, it would never be our point of view because we're, we're a multidisciplinary group.

We have partnerships with people like civil rights organizations and, you know, we're too embedded in the problem to think of it as just a mathematical exercise. I mean, we bring what we can to bear. And I find the, sort of the cold, hard mathematics that comes out of it endlessly fascinating.

And I like to play with that and that's, you know, I definitely get up in the morning wanting to do that kind of stuff, but it's a big point of pride for us that we try and retry and take the human factor into account in all of this. Because ultimately at the end of the day, it's about handing power back to voters and getting them engaged in democracy. Not about an elite academic class telling folks, this is how democracy should look, and this is how you should go about voting and go about your representation. Yeah.

Parmvir: Okay. So I'm cognizant of time and I appreciate you have a small human that your wife has been trying to get to bed. But we, we have a couple more questions. We've got one from Mike who says: can typical factors such as employment types or educational histories, determined political leanings about which to organize optimum outcomes?

Thomas: That is a, it's a big question. I think, I think that that question belongs to political scientists a bit too much for me to say too much about it.

There are definitely tried and true statistical methods to determine those kinds of questions, but the problem comes down to the unit problem. As everything is kind of being viewed  through a mirror darkly or whatever, it's through this aggregation up to precinct level. For example, one of the hardest problems in data driven political science is if an election takes place and you want to know, did folks race, do people's race play a role in how they voted? That's a really hard question to answer because we have the secret ballot, right? You can't take the ballots and go, okay, here's someone's race and here's who they voted for.

So, and you think that the way the flippancy with which this gets talked about sometimes in the media and in places that it was a done deal But you kind of have two choices, you can either try and do some kind of surveying or exit polling or whatever, which is fine. It has its own biases that they'll admit to, but if you want to learn a straight from the data, you've got to learn a lot of statistics. And it turns out to be a super fascinating space because every day in this country, there are folks standing up in court testifying about this race, this racial group voted this way. This racial group voted this way appealing to some pretty like subtle statistical models behind the scenes. So I'll say that our group is actually super involved in this space. We're currently trying to develop a Python package for doing this kind of analysis because it's historically been in a language called R, which is fine. It's totally fine. It's just everything else we have is in Python. So we'd like to keep everything in the one language. So that's kind of a roundabout answer to the question. Rather than saying, oh yes. And here are the relationships. I'll say that it's pretty hard in general because of the secret ballots, which we should to be clear, absolutely still keep no matter how much data scientists might want to, you know, it's a pretty hard question and requires some careful kind of modeling decisions, invariably you end up treating people in a very sort of simple in a simplified fashion in order to make your model work.

And you've got to account for that at the end of the day, because you could be wrong. And the question is by how much.

Parmvir: So yeah. It's not all about you, data scientists.

Thomas: Yeah. Well, I think so.  I don't know if folks know, but for the first time this year, the census is gonna mess with the numbers to add noise. And this is also something that, so you might have minus two people living in your apartment by the end of the process. So it turns out that the way the census has been doing things for years is totally hackable. Like you can, you can do checks, like realize that in this area, there is exactly one female head of household person of this race or something. And then it's a privacy concern. So what the census is instead going to do is like mess with all the numbers a little bit, but then they mess with it again to make sure that there aren't minus two people in your apartment, and, that it all adds up to the right stuff. And a lot of folks have a visceral reaction to this.

They're like, no, what, no, you can't do that. You can't, you can't count people. And then change the numbers. Data scientists are totally on board. We're like the numbers were wrong to start with. You know, if there's measurement error just, it's fine. We'll be fine. I mean, we'd honestly be fine with minus two people in your apartment. Like it goes into the computer just fine. As a number computer doesn't know that's impossible.

Parmvir: In voting terms. I mean, we can't vote anyway. So may we may as well be minus two people. So Austin asks, I understand that M G G G is non-partisan. How do you navigate questions about your political views when presenting your work?

Thomas: Yeah. We are very careful to be nonpartisan. We don't take money from Dems and we don't take money from reps. You know, we are primarily NSF funded. And we do occasionally, we partner with voting rights organizations who are sort of, so their mission is to just make sure that people are being represented and people aren't being denied the chance.

And so it is a point of pride that we are nonpartisan when it comes to your political views. I don't know. This is a tough conversation to have. I think that we definitely have values some principles that we stand for. We're not ashamed of you know I wouldn't sort of be shy about, about stating some of the values that we hold as an organization.

But in terms of partisan leanings my approach is always to try not to try not to bring it up in sort of research contexts, but you know, if you get me down the road, well, I'm so sorry. I'm talking about the before time. If one day you get me down the road at a pub in a better world then I'll be happy to share with you all my thoughts about what's going on.

Although I do try to temper it with the fact that I'm not a US citizen. So, it is a race I can't directly influence by voting. And it's also, I wasn't born in this country. I didn't grow up here. So I try not to sound to my own voice too much in those kinds of conversations. Yeah, it is a bit of a sticky wicket, you know, doing research in a political science arena.

But I think that the key thing is to know we have our values. We stand up for voting rights of minorities. That's a political issue for us. You know, we want to see the voting rights act enforced, and we want to see people be able to vote elect people who represent them regardless of sort of whatever minority status they might have, those kind of non political points we're very clear about. And then when it comes to partisan support, Maybe those are that's for the pub after the seminar.

Parmvir: Yeah. One would hope that that's the kind of thing that no one has any particular argument with, which is that if you're an American citizen and you meet all the stipulations, you should be able to vote. Right?

Thomas: Absolutely. And we're talking about gerrymandering that has vast bi-partisan support in the public for proper redistricting. Like no large portion of the public is really on the side of " we should gerrymander for my side". Like, I think I've seen a poll to this effect, but it's something I just believe in my bones that at the end of the day, you know, people want their party to win, but they're not interested in, you know, the way they can vote and who they can vote for being controlled by some people that are up at the top, right.

Politicians shouldn't pick their voters. Voters should pick the politicians, all that stuff. So in terms of antidote, I think we're talking to everyone at that point.

Parmvir: Thank you so much. We really appreciate your time. Honestly, the conversation was fascinating and we'll give you a shout at some stage when this is all released and upon YouTube, and you can feel free to share with your friends. Should you so wish.

Thomas: I definitely. Well, this was, this was a lot of fun and I think you all are doing a fantastic job. You know bringing science. I think science communication is, especially in this day and age when anti-science is a thing and folks are getting a bit getting a bit mistrustful and you know, this is, if we have another hour, we can talk about how, like this isn't all not awful.

It's like, you know, we in academia have we have some of the, some of the blame there, but I think that folks like you guys who are doing the job, trying to engage the public in science, it pays to have it. For, for everyone involved. So yeah. Keep, keep up the good work. That's what I'm saying.

Parmvir: Will do.  Right, thanks again. Good evening.

 [Musical interlude]

Thomas: I was switching from my masters to my PhD. I just arrived in Tennessee. I'm from South Africa. I was switching fields from category theory to essentially topology. I was kind of used to going to a conference a year, at least. And so I thought I have to do something to get myself motivated, to sort of make sure that I can go head first into this new research area.

So I applied for and got into a conference in Switzerland which was a bit of a wild ride because I was pretty much flat broke at that point. And they didn't like buy the tickets for me. They were like, we'll reimburse you afterwards. That was a lot of fun. I guess one of the reasons I was broke is coming from South Africa I saw my paycheck and I thought I'm rich beyond my wildest dreams. And then I saw the grocery prices and I realized, oh, wait, these two things go up together. Don't they? But I was in Switzerland and I only knew of a couple of people there, but the people, I did know were category theorists. Now category theorists have a bit of a reputation, which has completely undeserved, of occasionally thinking that they're a little bit better than everyone else.

So category theorists will sort of category 'splain to people sometimes. But the people I knew were two folks from category theory who I think are straight geniuses. It's like if one of them wins the field's medal, I will not be surprised, but these are people that were sort of just above or just above my level, maybe the same level as me career-wise.

But I was hanging out with them. So I was kind of at the cool kids table because I knew category theory. So we were all chatting a little bit. And at some point they said to me, "can you believe there's people at this conference who don't even know what singular homology is?" And I have this rule that I never pretend to know something in mathematics and it has, I think it pays off long term and I was sitting there and I was like, I could just keep quiet or I could speak up.

And so I, I said to them, "well, I mean, I don't know, what singular homology is" expecting them to sort of brush it off. And there was about two minutes of quiet and then they like, sort of, ummed and ahhed a little bit. And I tried to repair it by saying, "oh, well, I mean, I know the general idea"

And they were like, yeah, sure. And that was the last time I spoke to those folks at that conference. I think I'm exaggerating a little bit and I hope that they don't think unkindly of me for telling the story, but I did definitely feel like I'd lost my membership to the cool kids club because I didn't know a singular homology was, but I did eventually learn what it was. So I'm cool again.

[Musical outro]