 It's completely insensitive to the changing will of the people I assume that was that was like laughing in a home in a horror movie, right? So I could translate the previous one to be typical atypical atypical typical. Yeah If it's a quick question Yeah, yeah, just so So gerrymandering can occur even in the absence of oddly shaped districts Okay, so What about these startling results? So let's dig in a little bit more to this example this funny one the shocking Wikipedia example What I've done here is I've ordered the districts from most Republican To most Democrat in the percentages of votes Democratic votes they got So there are two that have 10% Republican Democrats and Three that have just enough Democrats to get over the 50% so that's how you do it. You pack the Republicans Oops, sorry. Am I doing it most red to most blue? Something switched. No, that's right So you pack all the Democrat all the Republicans in the far two districts the most Republican districts and you spread pretty evenly the remaining Democrats the blues across the others and that's how you create so it's cracking and packing. This is an example So what if we look at this vector and we try to understand the structure of that? so Let's put the other maps up there Here's some other vectors and now what we're gonna do is we're gonna look at each column We're gonna look at the column the most Republican the most red district and the most blue district and ask how typical go back to that question How what should the most blue district look like and what should the most red district look like there's no assumptions of symmetry here? It just may be that we live in an asymmetric world because of the structures of our states and our Interests in having geographically localized representation that tilts the balance in certain directions So if we do that We can make a box plot All right, what is a box plot? So box plot is a stat is a classical way to summarize statistics the far left is that most Republican district this is for North Carolina in the 2012 and 2016 elections This far left box plot is for North for the most Republican district in each of our maps So what the center line is is the median? The box holds 50% of the maps The whiskers or some idea of outliers and the very tips are the max and the min So you start to see kind of what typically should happen as some nice progression as it goes up It has a nice spread and these two look rather similar just one has been shifted down because the election was more Republican Let's take some maps that we think maybe are not so biased the judges maps from the beyond gerrymandering project the two Don partisan maps that were created on the 538 blog and let's put them on our graph Here they are They kind of follow pretty much down the middle not perfectly the yellow line down the middle is the median Connecting the medians. They're kind of tight But let's compare that so here they are I make a histogram. I measure the square deviation from the medians That's a number. We call it the gerrymandering index All right, and here the judges one are pretty nice in the distribution the other two are a little bit farther down But they're still kind of in the meat in the distribution. Let's go to the two that were used in the legislative elections Here they are. You see that huge jump That's the jump that causes this insensitivity to actual elections in a way That's what I think gerrymandering is it's that jump on this graph and there they are in the same histogram way out in the outliers Right and this is what Kagan so Eric Lander who was the head of the Broad Institute and a mathematician I Almost said originally, but one is never not a mathematician he's still a mathematician And he wrote an amicus brief that was based heavily on our work and Joey Chen's work and and Kagan Chief Justice cake not Justice Kagan. Well, that was a wishful thing Justice Kagan Brought up that brief in in court and and she discussed this idea of outlier analysis and now that's become a term Outlier analysis in the legal world people talk about it now Here's two other maps from 538 The one of them is tried to make it as most Republican as they possibly could and the other one They tried to make it as most Democrat as they possibly could there. They are see they both have jumps the jump is just in a different place That that loveliness and this large jump. So that's really kind of the trap the thing and here Okay, actually, so this is the plot. So how do you describe this to a bunch of judges? So I'm really a big believer in the way you convince people things with mathematics is you don't snow them You don't say here's a number. It's a p-value. It's bigger than this and trust me. I know what I'm talking about It's it's an outlier. It's bad. I Think that's not how you should do it what you need to do is you need to make the story Understandable so they can draw their own conclusions and they could see the difference in these lines Right, they could see that there was this huge jump and what's the industry with that jump meant? That was it. This was the actual slide that we showed in North Carolina and I showed this I gave this a PowerPoint presentation in court and We labeled the actual districts in North Carolina And that's important because one of the things that the recent ruling in the Supreme Court came down on and said you need to actual show geographically localized harm and so here we actually listed what North Carolina districts were harmed and there was a plaintiff from each of those districts in this lawsuit so Some people believe that we actually have satisfied probably the objections in Gill and the North Carolina court case will Move forward. We'll see we're waiting So we identified the cracked in the PAC districts these ones way up at the top are the PAC districts Where more Democrats were in than supposed to and these ones that were suppressed lower are the crack districts where they've been spread out evenly All right So this is the signature of gerrymandering. So here's Wisconsin So, how am I doing? I'm all right. Not great, but all right. So here's the act 2043 map That's the maps that were used in the general assembly election. So now we're switching to the state legislature in Wisconsin This is Gill versus Whitford. This is the main Supreme Court case These were the let the map that was used with a small caveat which I can it's a it's I'm being judicious and lying ever So slightly to you and you see here's three elections 2016 2014 2012 well two out of three elections. It hits it straight on the nose The other one does a particularly bad job right at the top one, but the other two straight on the nose Okay, two out of three. We're done. Let's go home. No problem, Wisconsin You have to dig in a little bit more if you go back and make that histogram like that set of Histograms like I did before again, they're right in the meat of things over all these elections But you notice all these elections are pretty Republican what have we thrown some more Democratic collections? So what happens is there's a firewall the minute you get to the point where you might lose the majority this map is designed either through intuition or through experimentation to Not let you shift Not pick up seats and it's exactly the same thing. It's the same thing that happened here See the reason this doesn't move is because whenever that line that 50% line if a dots above 50% It goes Democrat if it's below it goes Republican if you're one of the if you're the purple or the orange curve see Shifting the global election is just shifting this graph up or down You see how many percentage points you can shift the election and never move a dot over the 50% line a Huge window and that's what's happening in Wisconsin. It's basically designed that when you get there I'll show that to you in a second you have this Actually, so I won't show it I took it out for the for the interest of time But you can read on our blog we have a discussion of the firewall phenomena and that somehow comes back to this jump We also looked at Maryland. This is more preliminary results. We did this a couple years ago with some old code But now with some new code we just hop off the presses So it's not as shifted so these are the maps that were used the 2011 one is the one that's under question and you see it doesn't do a great job But not as bad as in North Carolina, but you see the same kind of jump You see that the far word now This is supposed to be gerrymandered in favor of the Democrats So we're looking at the far left this side instead of this side and you notice these dots of the far one are much depressed So in some of these elections it would have been reasonable that two Republicans would have been elected But the map is set up to only allow one to be elected So there's also gerrymandering in Maryland in the other direction. All right One interesting thing you if you've if you're at all reading the press about gerrymandering you hear people talk about the effect of cities versus rural effect because Democrats pack themselves in cities. That's the whole reason this is happening. What's nice is you can look at the two different effects and separate them So we can ask the following question in a given map How much would I have to shift the global election percentages so that it went 50-50? So in Wisconsin, there are 100 seats 99 actually in the state legislature How much would I have to shift the percentage to get so it was a 50-50 split in the? 2012 election that's the histogram for over our 24,000 maps of how much you'd have to split You would actually have to shift it to about 49 percent. So there is a bias to the Republican Party But notice where wi is You have to shift it all the way down there to make a difference So in the Republic in the 2016 or the 2014 election the structure the spatial structure the election actually meant that you You could only you could get the majority with around the equal partition with around 47 percent That's this one so you can see there is a bias based on where the Democrats live But this map you would only need 44 percent so you can separate the two effects Yes, there is something due to the geography, but this map went way beyond that Okay, so now I want to just say a little so you know this is a lecture that kind of gets a little bit more technical as I go So I want to but but at the moment I'm about to both become more technical and at the same time become current events like really current events so After Gill which was the decision that was handed down two weeks ago The ruling basically said that Wisconsin that Whitford had no standing because of there was no localization There was no geographic localization So as it happened we were already doing geographic analysis of these maps because we were interested Because that's what happens sometimes, you know you ask the right questions because you're scientifically interested and you end up with something that's relevant So we're gonna talk about something we're gonna do something a little different now. What we're gonna say is Instead of asking about the global precincts. We're gonna say I'm sitting in my district This is like kind of a Local model every time I'm sitting in my I'm sorry. I misspoke start reset your brain I'm sitting in a precinct and That precinct is sitting in a district in every map Right where it is exactly changes But every time I can ask what's the makeup of my district in this election? What percentage went Democrat for instance in that election and so I can kind of ask What's my typical environment that I'm in am I typically in a Democratic district? Am I typically in a Republican district? Am I sometimes in one sometimes in the other? What's the fraction? That's this histogram? percentage Republican vote in the district that my precinct is in Here's a map of it in North Carolina for the 2016 voting data the 2012 voting data You see that it and then what the coloring is is you take the log So it's a log likelihood and you plot it over the space So if it's more blue that meant that this district was bluer than I usually saw myself in and This precinct was in a district more blue in this one and if it's red, it's more red. It's more Republican So the Democratic districts have a much more Democratic than usual In both cases and there's a little bit of red The red it gets a little whiter here and a little bit redder in fact in some of these areas And those are ones where they took away some of the Democrat Republicans to fill Took away some of the Democrats to pack them in these other districts so you can see that effect But then you can sum up this log likelihood You can look at the spatially average log likelihood and you and here I have it plotted with a different color scheme Which I actually like better like I said, this is fresh off the press and here I have another histogram. So my fancy Collaborate if you make fancy pictures This is Jonathan in Jupiter to your left. So you get the ugly pictures now So here's that histogram again and the judges are right in the middle of the meat They have a very low log likelihood. So the log like is just the log of this probability It's a way of measuring if it's big Right because if you take the log of a number between zero and one After you center it one half if it's big if it's away from the median It's it becomes a big number if it's near the median it becomes a small number We've centered around the medians and these two maps are unusual so what we're starting to see is a way of of of measuring localness local harm another way you can measure local harm saying is how often are Their districts which are really outliers which they're in a district which looks completely different than what they usually see themselves in So we counted the number of 95% outliers and the judges map has very typical number if we average over our ensemble That's what this blue is and notice the two maps that were used in the legislature in our elections We're very unusual and if you look at the districts that were outliers They pretty much correspond in some ways to the Democratic ones But there's also some noise which is something we have to explain to the courts because when they look at this They want there to be no outliers Right, but we know that doesn't happen right there's a famous probably hypocritical story That's often told to me in that I've heard more than once which is that there was some study in New Jersey And they found us a mile of road that had a huge number of accidents and they were commissioned a huge study of why that happened But of course if you think about it, how many miles of road are there in New Jersey of Interstate and what's the chance that there's one mile that has an unusual number of accidents It would be actually very unlikely that there was no unusual mile So it's much more likely that there was nothing wrong with that mile of road It was just that that was the one that it happened it So you have to have you have to always benchmark things and think about it. Okay, so Let me end with some open math questions This didn't seem like a math talk, but maybe hidden in it is there was so Oops no math questions again. Here we go. All right, so Here's a very naive random state, so let's let's pretend our state to consider a state Which is a Taurus what I mean by that What I mean by that is it's it's it's video game mode you go off this side You come back in on this side you go off this side you come back in on this side It's asteroids. That's even you know what a Taurus is you have no idea what asteroid is asteroids. Anyway, it's video game modes You run off one side of the screen you come back on the other Then let's make up a random a random political distribution of a party Sometimes we've done this two different ways. I have a student a high school student who's dropping random spheres With some drop off from them This one here is actually a random for a series. Sorry. I didn't do that for you, but it just so happened I mean what else would I do right and then you want to do divide this into nine districts? Well, guess what the isoparametric division of a Taurus is into nine districts that and there's a number of them, right? Because you can just shift it That's why I picked a Taurus because now there's no problem to enumerate them. By the way the best enumeration algorithms died around 30 40 precincts So we can't just count them all But maybe somebody can figure out a better way and we can count them or a smart pruning algorithm So if you're discreet inclined, I have a collaborator chapel who's thinking about that So let's run over all these districts. Let's see what the elections are and we get look at that We get a box ball that looks just like what we saw So then the question is can we understand what the properties of this field are that if it's a generic realization of This field so that we get this box plot and what sets the scale if you were to just pick each precinct Randomly from a distribution the scale is much more collapsed. What sets this effective length? That's a math question Another math question is why is this ridiculously stable? So I've been showing you these box plots that all the information comes from here's a case where I Shifted all my weights up or down I think it was 20% I Changed some of the population energy is to slightly different definitions Qualitatively the outcome looks the same. It's not surprising. I mean some huge dimensional space and I'm projecting it down to 13 marginals Maybe there's some concentration measure phenomena going on here, you know, what's the lips just constant on my maps? I'm not sure actually I thought a little bit. I have some ideas They're stupid, but maybe there's a better one. Can we can we do something here? even more is This a replica symmetry is this or you know one RSB phenomena where I have lots of different identically almost identically looking minima Which have different properties and it kind of doesn't matter where I end up Because they all look kind of similar and they're just shifting around so maybe that's what's going on I don't know. There's some reasons to think that's true. It happens in related pots models Yeah, here it was can you pot can you plot the energy landscape that this energy functional gives you? Can you give me some understanding of that? I Have a weird surface energy. I have a weird bulk energy. I have some global constraints Can you show me some evidence of a shattering? transition it's a little technical but in any case On the numerical level, how do you get better samples? We're not thrilled with the samples we used in court. They're okay We're working at better ones. We're trying to use techniques borrowed from computational molecular dynamics to do a better job of this and We're trying to understand how to speed those algorithms up and so I did not do all this work This is a team effort So it started with myself and Christie Graves now Christie Vaughn. I'm sorry Christie Graves now was Christie Vaughn Got it backwards. Sorry. She's now at Princeton then the next summer There was an undergraduate team that Christie was part of was Sachet Sophie and Bridget and that was a program We called data plus in 2015 and Christie's thesis was the year before in 2014 And then the following year Justin Lu and Hong Song Han And by the way a lot of these people are actually North Carolinians or people from the southeast So they were politically invested in these questions And now there's a group of a graduate student Robert Revere He just graduated actually Greg Herschelog was a postdoc and now it's kind of a senior researcher And the reason there's a red box around him is that he's really been yet my real collaborator really doing consistently over the last couple years lifting and getting things done Mike Bell is a Geometer who's interested in this and then there's a new undergraduate research team of Lisa's a master student and Sam Lisa and Raoul and they're part of this data plus 2018 undergraduate research project. So all most of this work the original code was all written by undergraduates The latest version Greg wrote but you know, there's there's a lot of work and next year We're actually running a course on this at Duke So I have another group of undergraduates 18 of them taking this course a research course a research independence study and working on this So we'll be interested to see what happens and these are all the people who gave me money You notice none of them are yes, somebody quickly notice what is not on the list these are all private entities and more or less and There is a website Google Quantifying gerrymandering at Duke and you should find it rather quickly And if you have more questions, I'd be glad to talk about it And there is a summary slide, but it's kind of boring. So instead let's see if I Go out of here, and I go to not that to this There we go And now yes, I haven't backed up. I've been here. Thank you very much. Okay. We'll just leave this running. Well, I'm happy to take any questions. Oh Interesting, right That da da da da da da da da da pause Okay, one second. How do I do that? one second I Have to let's just mirror displays Now you'll see momentarily my whole life and let's Go over to here and now let's make this bigger Is that how does that look? Play go there we go finds the conflicted edges picks one out flips across it goes goes goes It's checking to make sure the past stay contiguous So if you're wondering why it never breaks because it's rejecting moves to do that And so this is a little app in Java you can load in From my website and look at if you want to and I'd be happy to take any questions if you happen. Thanks a lot Thanks, Jonathan Before we before we take questions, I have to observe that you know you have 1800 unanswered emails I'm looked at emails which explains quite a lot about why you never read my emails, but Okay, so questions, please Well Better I mean, I think they think they did a very good job. I mean, I think they're very happy with the map They chose right? I mean when they wrote what no, let me let me explain to you why the North Carolina case is such a clean case There's no question of intent. They actually wrote a document The state legislature did which was directions to the subcommittee and the map maker here The things you should follow this this this and you should end up with a map They gave the same political outcome as our previous map, which was which was for 9 or no no is that at that by that time it was already 10 3 10 3 and somebody asked them on the floor in the official record. Why do we use 10 3? And he said because I tried to do 11 to and I couldn't and that's on the record of the state legislature, right? And and and he got up the mat maker said let me be very clear Since you ruled our previous map an illegal racial gerrymander. We are and this hasn't we did not use race at all This was strictly a political gerrymander. That's what they said So I think they think they did a very good job. So I think the difference in the maps was simply Intent and what they wanted But they were optimizing to be at the worst right they were very close to the map Almost said, you know, not identical spatially but outcome wise to the map that 538 gave as their attempt to optimize To make the most Republican map possible Okay question back there Flesh or question out not likely I mean not likely that kind of depends on who was in charge Well, but see that's not about a state of them. That's not a I see you're saying of a certain redistricting Yeah, right. Okay, so so right so that's a really good null hypothesis question to ask the right, right? I mean so It's actually rather labor-intensive to get this up and running on a state We did do some with a preliminary piece of code. We did some work. We looked at Iowa Which has a there are a couple states that have a different method Iowa, Arizona and California have either non-partisan or bipartisan redistricting commissions Iowa's do not seem so bad. Now. You could also attribute that to the fact that Iowa is a square state with four districts Anyone want to guess how they did it? And and by square I mean rectangular because I'm that kind of mathematician, right? There are three kinds of mathematicians those that can count and those that can't So what do you mean by dynamic flush out the word dynamic? I mean, I think you need to you need in some way take into account the effect over a number of different elections You can't fix one election unless you look at this fine-gain structure, right? It may not affect a particular election you're looking at but it could affect other reasonable elections That's one to I think that things like partisan symmetry or the efficiency gap Which try to which they themselves postulate certain things that they value But they don't be explicit about it always and they're not they never take into account the geometry at the state And by and I mean geopolitical geometry like who lives where the structure the population densities They don't take that into account. I think that doesn't make sense I think you have to have some way of taking on your account And I think the only realistic way to do that is some type of controlled sampling where your Where your assumptions are very explicit, right? I was very explicit about what my ensemble cared about these things only right, yeah, I mean Right, I mean, it's just gradient descent with a smart stochastic gradient method You just do exactly what I did. I gave you the energy optional. You just flip some signs Yeah, sure, right, right. So that mean and that's in some sense what they do Maybe I don't know how much I know a friend of mine wanted said like maybe we should just get out of this And we should write a you know a plug-in to the mapitude which is the software they use and you know Jeremy and or my state, you know Have a big red button I mean, but you could seriously do that. You could say relax this locally, right? It's just a variational calculus problem Relax locally this to gerrymandered as much you want, right? So I of course Sutlana they can do that and that's part of what's going on in it and using local knowledge and in some sense Hand manual gradient descent, right? Let's change this. Oh, that helped. Oh, what if we do this too? Oh, that helps Oh, yeah, yeah, right. That's what they're doing They I don't know how automated they were Well, they did hire professionals, right all the maps in in they hired a there was one map maker that was hired by the National Republican Party to do the local state maps and was hired out to states all over the country in the 2010 and That accounts for some things that happen so partially so, you know, I Don't know people who are explicitly doing that now. I mean, I think you could easily I have the code to do it I could do it but They in some sense, they didn't need to they had enough local knowledge that they could get in a neighborhood of a good solution and Then by local tweaking they could end up with one, right? They didn't need to be quite so they weren't writing a paper They didn't have to be quite so systematic They needed one example and they could do it by hand and they they read they admit that they made tons of maps Wisconsin, I think admitted that they made lots of maps Back there, but I'll just say that's kind of why we have to do this, right? We have to come up with a way to inform the government to to be able to clip out the outliers So that we can identify them and clip them out exactly because it's easy to do. Sorry You caught me. Yeah. I mean, I think this is all math Okay, so I'd say that say a lot of things How long do I have rave? All right So first thing is I think most people when you ask them what the math is they'd ask you to balance their checkbook Or figure out the tip. Okay, so I would say that's actually not math What math is is kind of a systematic conceptual framework that's that's built thinking carefully And I think that this is very much math what I'm doing, right? So I think this is math and what I meant by where's the math? I really should have maybe said where is the Mathematization of what I had previously said because that's what I really started to give you at that moment, right? Just one second. So so that's one thing to I think that You know what I'm the chair of my math department And so I talk a lot about what math is and I think that there are that that that you know mathematics in the past had made some errors about in in in In crusades of purity throwing certain people out of the tent and that was bad. I think the real question was you know just Step up to the plane figure out how to make it all work as one family and how to live with the continuum And also I will say that in my I think of the mathematicians inside my department and the mathematicians outside of my department There are plenty mathematicians at my university who are not in the mathematics department and who are essentially part of the time or all the time Cartel mathematicians right and so I think that that there's a huge spectrum of what mathematics does Okay, that's part of it And I also but I also think that it is important for mathematicians to periodically step out and find new problems of Societal interest or of scientific interest and bring them back to the math community, right? There have been moments of explosions like that, you know physics that led to calculus That was one where there are all these questions that we that people need to figure out There are other moments like that, you know, maybe large data is another moment like that, right? So more