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The Intersection of Mathematics and Democracy
3.7k Plays4 months ago
This discussion Autumn and Gabe delves into Ismar Volic's personal background and inspiration for writing the book, “Making Democracy Count” as well as the practical and theoretical aspects of voting systems. Additionally, the conversation explores the application of voting systems to everyday decision-making and the use of topological data analysis in understanding societal polarization. The conversation covers a wide range of topics, including data visualization, gerrymandering, electoral systems, and the intersection of mathematics and democracy. Volic, shares insights on the practical implications of implementing mathematical improvements in electoral systems and the legal and constitutional hurdles that may arise. He also discusses the importance of educating oneself about the quantitative underpinnings of democracy and the need for interdisciplinary discussions that bridge mathematics and politics.
Keywords: math podcast, creativity, mascot, background, Matlab, ranked choice voting, elections, author's background, inspiration, voting systems, topological data analysis, societal polarization, mathematics, democracy, data visualization, gerrymandering, electoral systems, interdisciplinary discussions, practical implications, legal hurdles, constitutional considerations
You can find Ismar Volic on Twitter and LinkedIn @ismarvolic. Please go check out the Institute for Mathematics and Democracy and Volic’s new book “Making Democracy Count”
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Transcript
Introduction and Podcast Updates
00:00:00
Speaker
Welcome back to Breaking Math, folks. Today we're venturing beyond the realm of peer numbers and into the fascinating intersection of math and democracy. I'm your host, Autumn Feneff. Joining me is my co-host, Gabrielle Hatch, and Ismael Volej. A professor of mathematics at Wellesley College and director of the Institute for Mathematics and Democracy, whose work explores how mathematical tools can be used to strengthen the democratic processes. Ismar recently published a book, Making Democracy Count, which dives deep into this very topic. But before we dive deep into today's episode, you can support us by signing up to our Patreon at patreon dot.com forward slash breakingmath.
00:00:44
Speaker
We've also launched our new website breakingmath.io, so we highly advise you to go check that out. We also have updated some of our social media handles and uploaded a lot of videos to YouTube. So if you would like to find us on YouTube or Twitter, X, whatever you want to call it at this point, you can find us at Breaking Math Pod. But if you want to find us on Instagram or TikTok, you can find us at Breaking Math Media. We also have a Facebook community, which is Breaking Math Community. In addition to that,
00:01:24
Speaker
We have an open call from mathematicians, scientists, and engineers. Pretty much anyone who would like to talk about their work. So feel free to email us at breakingmathpodcast at gmail dot.com or fill out the link in the show notes below.
A Refugee's Perspective on Democracy
00:01:42
Speaker
Now, on this episode of Breaking Math, you can join us as we take apart our election system mathematically. But first, here's a message from our sponsors.
00:02:02
Speaker
Thank you. Those are very kind words. As you know, mathematicians aren't used to this kind of attention, right? Like we write our papers and books and then three people read them and but or not. But this is quite this is like sort of some next next level engagement. And it's very it's very gratifying and wonderful. And I and and I love doing it. But yes, I come from Bosnia, which, you know, as you might know, went through this horrible war in the early early 90s. And that's when I came to the U.S. as a refugee. And so I was always aware of how how bad the and ah democracy can break down. like so I've seen like the other end of of demise of democracy, right? Complete with like genocide and atrocities and war and killing and everything and all that. So I think it's when democracy started really breaking down the risk country over the last some number of years, but really it it affected me maybe differently than than than it would
00:03:00
Speaker
would have someone else. And to this to this day, right, I see things that are happening right now in the U.S. and across the world. Just the U.S., you're sort of the the leader in it. But still, it's it's happening across the world. I can see the potential for how bad it can it can get. ah uh... so that's one of the reasons why i wrote this book if it was my way of of contributing to to to make you know making things of a little better in the only way that i knew how i've always done mathematics and i love mathematics and you know i could have been engaged politically maybe in some other ways but this is really the optimization of my of my knowledge and my expertise to to to to marry these two things you know creating a better democracy with
00:03:45
Speaker
but but based on sound mathematical processes and and evidence.
Understanding Ranked Choice Voting
00:03:50
Speaker
So that's how my background as an immigrant here it was kind of folded into this into this book and everything else that I do in the space ah of ah of math and democracy.
00:04:03
Speaker
Nice, nice. I think ah for those who are listening to this podcast episode in particular, and who may not you know who may not have read your book, um I'd really love to introduce some of the topics. you know and i think either I don't remember if it was your preface or your first chapter. You start with a very, very basic example. And it was extremely, extremely helpful. And the basic example was just simply ranked choice voting. And if I recall correctly, the the example you chose was your daughter going to school and what movies they wanted to watch. um Again, for the sake of our listeners tuning in, can you go over that example or any other similar examples you've thought of in the meantime, just so that the this so that everyone's on the same page with what ranked choice voting is?
00:04:43
Speaker
Right. So that's an example that every time I talk about this stuff, all my talks either start or end with this example. When my daughter was in fourth grade, the teacher said, you know, Friday, we're going to watch a movie, you but you you behaved well or something, right? Come to school in pajamas, bring your favorite toy, we'll watch a movie. And and she said, we'll vote on three options. And they were, I found out correctly, bold and and incredible. It's two and co-co, right? So this is, my daughter is nine years old at this point, right? She's in eighth grade now. But, and I said to her that Friday morning, I said, why don't you ah try to remember how the vote turns out? just Just tell, just let me know if you can. And she comes back from school and sure enough, she reports that, and I'm going to get the numbers wrong now.
00:05:30
Speaker
I don't remember exactly how they went. But I have the book here. All itself. I don't know if you've seen it. Oh yeah. he was We all got our copy. Bolt got seven boats. Incredibles 2 got six boats. And Coco got four boats. Okay, so seven sticks at four, right? And the teacher said, yes. Well, you know, both have the most boats and not much boat. The problem with that is it's really the fundamental issue with All the mathematics underlying democracy, and there's a lot of it underlying democracy, is that this is not really necessarily presented of the will of the majority. Right. Because more people, 10 I guess, is that right? Did I say 6 or 4? 10 people!
00:06:14
Speaker
did not have both as their first preference. So in a sense, the will of the minority had been imposed on everyone, right? Now, maybe these other kids also didn't mind watching both, right? Or maybe they really hated both and would rather like, you know, but i don't do their laundry and do dishes at home, they watch both. But we don't know that the system did not gather enough information for us to be able to tell that. And so what the teacher could have done is she could have done a little run-off election, which in this case, in the case of three candidates, three options is equivalent to instant run-off, basically eliminate the the but the ah option with the fewer first place votes, which would have been Coco, four place votes, and ask those four kids, well, we're not going to watch Coco. It doesn't have enough support.
00:07:06
Speaker
But who would you like to, which movie would you like to watch it in? The remaining two options. Both Incredibles 2. And those four kids, the depending on which which movie they chose, the results could have turned out differently. Maybe both wouldn't have come out ahead. Maybe Incredibles 2 would have come out ahead. We don't know that. We just did not. The algorithm used, namely just your reality of all being first past the but post, when you just choose one option and that's it. and then you tally the number of votes that everybody got. That algorithm, which is a mathematical process, is is not sufficiently robust. It does not collect enough information from the voter in order to make an kind of an optimized choice that represents the will of the people, right, in in some in some sense. and the ah the the the And the funny part of the story is that my daughter actually
00:08:00
Speaker
went up to the teacher after after teacher declared bold to be the winner and said well maybe we should we should like you know do something else because there are more people didn't want bold and she tried explains to explain the ah to the teacher this is my daughter gory right nice and the teacher got mad and sent her back to her seat now um I'm always on the side of the teacher, and I am even without way without still on the side of the teacher knowing my daughter. I'm sure this conversation didn't quite take place in as nice a way as my daughter would like me to believe. But it was a missed opportunity, right? fourth A fourth grader understands that there's something off with the selection system that just took place. This was a teachable moment, like a little civics lesson you know like wrapped up in a little bit of math.
00:08:52
Speaker
that a fourth grader could completely understand. And this this is sort of the agenda the the starting point for um for my book and for it basically, again, everything that I do in this space is that we really lack this kind of education. Political quantitative literacy, is there is there is none of it in our schools. And unless that starts happening, it's gonna be hard to to implement or bring about my mathematically better democratic system.
00:09:22
Speaker
Yeah, awesome, awesome. Now, with that being implemented in schools, what ah in general, why do you think this is so crucial for any sort of voting, any sort of democratic process?
Mathematics in Democracy
00:09:40
Speaker
I think it's crucial because most of our democratic, most of this democratic infrastructure that we have, the underlying processes that power our democracy are fundamentally mathematical. They're always reduced to some kind of an algorithm, equation, process of counting, tallying, decision making that's quantitative in in some sense. So really, in mathematics underlies all these things. right So it's not just voting. Voting is the big topic. right But you know when you think about the electoral college it and how that mathematically plays into the into the choice of of our president, when you think about apportioning legislative seats at every level, like congressional, state, local,
00:10:19
Speaker
the rounding rounding to the most optimal number of representatives that you're going to allocate. When you think about ah districting and the geometry of districts and gerrymandering that goes along with it, which is you know one of the greatest threats to our democracy these days, gerrymandering. so All these processes can be analyzed and studied using mathematics. And at the same time, mathematics can tell us which of those processes work and don't work, which need to be updated, which need to be completely replaced with something else. So there's a ton there and that's mathematical and where mathematicse mathematics can can help us set things up better.
00:11:01
Speaker
And there's so many questions. there i don't I don't even know where to begin, because you know there there among the questions I have are not only ranked choice voting for people, but then I thought about, OK, you could also have ranked choice voting for issues as well. Now I know that that party issues are pretty well defined, and that's defined pretty darn far in advance. And you could even trace the pipeline for when any given issue suddenly becomes political, you know for for example, electric vehicles. you know i mean like We know what what party is for them, what party is against them. And it's a matter of of identity. yeah and i mean So I guess one of my questions um is I wonder in what ways, not only in direct elections, but in other ways, ranked choice voting can be used even for informing you know the temperature of the public on any given issue or or just ah or even issues just across the board. You know what I mean? I guess m may my question for you would be, um in terms of a participation or a participatory democracy, are there
00:11:55
Speaker
Are there other unique applications for either ranked choice voting or any other sort of voting that you can see would be helpful to diffuse the temperature in America specifically? and That's a good question. I'm not sure I thought about that beyond actual sort of elections of of officers and in in in public office, of which there are over half a million elected officials in the US. That's a lot of ah's a lot people we like using mostly. a terrible system. But any I guess i would I would answer sort of the most generically because then I'm a specific example in mind. But anytime there are more than two options presented somehow on which we'd like to express our preference or opinion or and or anything else. So the ranked choice voting is a is a reasonable system who to to implement.
00:12:47
Speaker
It is just simply might make more sense to ask people not just what your favorite thing is, but what is your favorite thing, and what's your second favorite thing, and what's your third favorite thing, right? That that the definitely ah puts a kind of a ah ah finger on the on the pulse of the opinions ah of the opinion the the public in in in any situation that that you might have. So, you know, this for legislat legislature deciding how they're gonna allocate funds to social programs or something, right? There could be a ranked choice vote that that sort of captures the the the will of the legislators a better. If we you know elect people to committees in companies or universities, et cetera, right
00:13:35
Speaker
We should have, we typically have multiple options. We should be ranking those options, right? both The rankings themselves are going to tell us a lot more about how the community feels about the options, about the choices, regardless of of of who wins. We might see that. someone who we thought is not a popular option is actually getting a lot of second place votes. say right So they're not winning, but we we recognize that there's something there. People actually are interested and in this option, which didn't seem to be viable. And this option gets the message that yes, they're viable. Maybe in the next election round, they should you know they should engage even more. They should look for more resources or put more resources into a certain kind of
00:14:21
Speaker
campaign or something. right So that's just a lot more information is just that. When we're doing the ranked choice voting, essentially it comes down to a couple of things. what The misconceptions that people are going to have with ranked choice. um you know It's your first choice, it's your second choice, how do we play that into effect, right? And then the next thing that you think about with that, we have our theoretical mathematics and then our really practical implementations in the book. um Theory and practicality sometimes go hand in hand. Where does this fall? Because, you know, some people are always skeptics. Oh, they're trying this new thing, right? How do we gain that trust? How do we gain that
00:15:07
Speaker
proof Well, yeah, that's also a great question. There's a couple of questions here. First is, how do we talk to the public about this, maybe, and how do we convince the public that that this is the right thing to do? And second is, how how do we, on the theory side of things, feel about this as being sort of the right the right thing to do? right And and those are those are separate and related. so i we experience has shown that any time that a person is willing or receptive to hear about dangerous voting and what it does and how it works, they are on board with it, but by and large. So it's all about indication, explaining that this is, you know, you're you're getting better pick a better picture of the electorate's will,
00:15:51
Speaker
and Anytime people hear that, again, for the most part, they are on board with this. Now there are some ideological ah resistances that are happening, especially recently because ranked choice is becoming more popular and hence the opposition to it is getting more organized and more vocal. But the opposition is typically along the lines of like, Why are we doing this? We've always done this other voting method. but What's this new thing now? Why are you like doing this to me? It looks complicated. Exactly. So I think education is is the right the but right way to approach that. And in a tiny old part, that's what I hope my book would would do because it does try to really dissect these voting systems.
00:16:34
Speaker
and be clear kind of the best one in a most ah objective, formal, mathematical, kind of detached way, right? and We're detached is the good thing now, right? There's no politics, there's no opinion, there's no ideology in anything that that I write. If that message can be brought to two people, I think it's very successful. Now, there's this other part of the story, which is academically really interesting and really cool, but we probably shouldn't bother a person in the street with it, right? And there is this discussion that we have as mathematicians, which voting system is best? Because when we say ranked choice voting, what we really mean is,
00:17:15
Speaker
Rank choice voting just means people are ah ah ranking their preferences. They circle the first person, and second, third candidate, fourth, and so on. Now, there are various ways of tallying these ballots, these rank ballots. And one of the ways is the instant runoff way of tallying rank ballots. And that's what has become synonymous with rank choice voting. That's sort of the most popular way of tallying ranked choice ballots. But there are other ways that you could tally the or or pronounce the winner out of the same set of ranked ballots.
00:17:51
Speaker
So there is you know you can assign points, for example, to the ranking. So that's called a board account. You can extract um pairs of candidates and compare them, how they do against each other. And if there's a candidate that wins all the headto head-to-head contests, that's the winner. So that's called the Condorcet method. night And there's a slew of other methods. And here is the part that's frustrating and fantastic and exciting is that all these methods could give you a different ways. Right. So this is not what you want to go into the public with. You don't want to muddy the waters, right? Precisely. yeah
00:18:30
Speaker
Well, there is this, there was this kind of like internal bickering among experts for the last seven years as to what method is best, where best has to be defined, obviously, on formal, like schematic, you know, postulates way. And this is the genesis of social choice theory that it goes back to the 1950s. And it's still a very active and and lively area of research. um But what we see, what we seem to be kind of coagulating around the the community of mathematicians, economists, statisticians, data scientists, political scientists, is that in Instagram not is sort of as good as it gets. We have enough now empirical evidence from lots of rank choice elections that have occurred over the past 20, 30 years, because lots of, you know, lots of places in the US s do rank choice, even if we're not aware of this.
00:19:25
Speaker
and ah countries, other countries, like Australia, New Zealand, Scotland, et cetera. So we have enough empirical evidence to see that is the runoff, it's not perfect, but the ways in which theoretically it could fail and fail in a sense that could produce kind of strange results, that that happens extremely infrequently and that we don't really have to worry about. So that quick term i'm sorry yeah go go ahead since quick term definition for those who have not read the book and may not be aware, can you explain what instant runoff is with respect to um um everything else we're talking about? Right. So just to run up but so again, it's if you have a but a bunch of ballots where people have ranked their options, very second, third and fourth. So the instant runoff works is if they're if someone wins the majority of the first place votes,
00:20:20
Speaker
They're the winner. So any time you cross the 50% threshold, you're the winner. If there isn't one, which would happen if you have three or more candidates, right? Maybe nobody won 50% of the first place votes. Well, then what happens is you take the purse the the op the candidate with the least number of first place votes. and you eliminate them. You say, okay, this can't be the winner. Just like Coco, right, who had the the least number of first place votes in my daughter's fourth grade class, so that gets eliminated. Now, anyone who had that eliminated, now eliminated option as their first shape the first choice, their vote gets transferred down to the second choice on their ballot.
00:21:05
Speaker
Right. So that second choice now becomes their first choice. So there's a retabulation that happens here where all the everybody's votes for the person that's been eliminated are moved down to the next person on everybody's ballot, right? So this bears with this there you inherit these votes, ah ah the person next person on the ballot inherits your vote. So your vote continues to contribute in in some way, right? So you could vote for an option that's a third party candidate or a minority candidate because
00:21:40
Speaker
you just you want to support them even if they have no chance of winning right but you want to send a message that this is the person you like best without fear for example that it will waste your vote Because if they have no chance of winning in a plurality election, you will have base to your vote on that, right? Your vote, they can win. So you just, but in an insta one off election, your, your vote continues to contribute rights. So the person is eliminated, but your vote is transferred down to the next person in your list, which might be a mal major candidate. And now you really are bringing, ah bringing your vote into play.
00:22:17
Speaker
So it really, and this continues, this iterative process where continues until someone gets the majority of the first place vote. So that's sort of it in a nutshell.
Family Dynamics and Polarization in Voting
00:22:29
Speaker
Nice, nice, very good, very good. The example that we used growing up, so i I grew up in a house of four brothers, so as we're having this conversation, as I read read the book, I thought about every little game theory rule, rule every all of them, that you know between me and my brothers, including I call shotgun, you know if you're going to get and into that's to whoever calls it first, obviously, but one of my favorites is any time we were serving up ice cream, ah one person would be in charge of serving up the bowls, then the other person got to choose which bowl they they that they took. so
00:22:57
Speaker
yeah you know that co that's the cut and tune cut and choose method um ah yeah theory i was gonna add i thought you were gonna say you did a lot of prisoners the lemin game theory like are you goingnna rat on your brother i think about ratty and each other or not yes Yes, and that's hilarious because there were times where we were a united front against my mom And not all, every once in a while, now I'm a parent myself. I've got five kids. And every once in a while, parents can make mistakes. You know what I mean? If we could clearly see, yeah, if brothers, when we could all see that the parent made a mistake, like say that somebody did their best or somebody made a mess and it was an accident and they got in trouble and it wasn't their fault, we would be a united front and we would figure out ways to get
00:23:45
Speaker
you know, whoever out of trouble. but But that was when we had the perception, the shared perception, that there is an injustice. And then also, obviously, we're already brothers, and I think there's a natural um a natural kinship there, you know, obviously. So in the question, you know, is it it like, like when what when is there a kinship? When is there a shared interest? You know what I mean? Like, um and that that I don't know. I don't know. That's all part of ah yeah how we as humans form societies. So I just wanted to bring up those examples because there's just so many ways that there can be an agreed-upon set of rules where there's at least an activity that can exist, even if it's a society that can exist. Because, yeah, it's been it's been tough lately. it's been It's been tough, you know?
00:24:25
Speaker
but there's no um and but anybody read I mean, these, did ah I'm sorry, just to interject a little bit, but did these principles and and algorithms and and the way of thinking it applies to the you know dumbest things, like where are we going to go to the restaurant? Well, let's rank some restaurants, right? Yes. You really, you secretly, we're not such a, you are ranking restaurants, like, let's do Indian, but let's India, is it open, is it closed? I feel like India, well, our next choice is, you know, Mexican. so You know, so you're naturally, ranking your options, even without realizing it comes naturally to us. So this is why I feel like scaling it up to presidential elections or municipal elections, any kind of elections, right? People are used to ranking things, so I don't think that's a big deal. Anyway, sorry to interrupt, go ahead. No, no, I think that's great. I think that's great. Something else, pardon me for all these little peripheral angles here, but one other big issue in my own family that almost leads into huge fights when we're talking about politics is people who are very strong single issue voters. Like really, like nevermind anything else. And it's brought up the question for me, you know, I'm like, well, number one, I disagree with you. And again, I shouldn't judge, you know, there are times where maybe there should be a single issue vote. I don't know.
00:25:39
Speaker
I don't know but but I just wonder like like how can you I don't know how what would be a way where we could have a voting system where where you wouldn't even have a single issue but I realize that's kind of a peripheral question but but it's still a legit question you know. And I don't know for it. So that so that probably have to do with the, you know, with how politics is presented to us and and and what the propaganda is, what the media are emphasizing. We're not emphasizing. So that's probably a less of a mathematical question than just kind of the state of politics or politics questions. but But yeah, I mean, you could you could have people voting on different issues and try to kind of um aggregate the answers into into ah into a bigger bigger picture. I'm actually doing a cool project now where ah where the students, a couple of students and are analyzing. So Pew Research does this political topology surveys every three years, and they pull people on a number of issues that are kind of timeless, not issues of the day, but sort of ideological pervasive kind of like longitudinal issues. and And that's what we're trying to to sort of set up this
00:26:48
Speaker
topological data analysis approach to this where we can tweak certain issues, turn them on and off and see how the geometry of people's opinions actually changes. And we're hoping that will give us more insight into polarization and where coalition coalitions might or might not form and and where where really the the holes are in our in our in our polarized society, where the true essential holes are in which holes can be kind of plugged up. So but that's also a peripheral comment riffing over your question. but yeah I would have never thought about that with the data and how that works with topology. Oh, that is interesting.
00:27:33
Speaker
there's There's this whole field of topological data analysis that was developed in the last, say, 15 years, where you just try to regard a data set as a topological space, and then you study it using topological techniques, you know, these invariants like homotopic groups, homology groups, and then you try, and and they tell you things like, oh, this thing has a three-dimensional hole. Okay, well, then you go back to the data and say, what does that mean in terms of the data, that there's this hole, that the geometry is informing sort of relations in the data that that classic classical statistical analysis can't quite do. And it's been really ah ah ah really a fruitful area of research. So that's off on the tangent. But as you can see, I'm excited about it. Oh, we got some awesome tangents. We could even rank our tangents for the best tangents of all time. Sometimes that's where the best dialogues come from. you know No, I'm serious. like You can prepare all you want, but sometimes it's the tangential stuff. you know no Are you a fan of the Reddit page, Data is Beautiful?
00:28:30
Speaker
No, I'm not aware of that. okay So people will who are obsessed with with Excel and spreadsheets and representing data, they will do any kind of data that you can think of, whether it's it's you know how you fit socks optimally into a suitcase. or or like um ah You know just the like like people watch at their campus and and just any sort of random nerdy data and they will present the the data in all kinds of gorgeous ways with sequence and patterns and show you how you do things and It's cool. It's just it's just really really cool. So that's gonna be cool and like probably there's cool visualizations, right? Cuz that's all the rage I like visualizations of the beta check it out
00:29:12
Speaker
ah very cool like I would highly recommend it because when you're looking for an undergraduate niche project or any weird topic, you can find it there. yeah yeah yeah yeah it's just just the as sortted in fact There's got to be a self-aware meta thread in data is beautiful. In fact, let's go there right now just for the heck of it. Let's just see what's on. No, it's worth it. It's fun. It's actually perfect. If you look at the second thing that there, it's about Champions League finals. Okay, which is what I was talking about is happening at 3 p.m. Yes. And that's the current topic, right?
00:29:49
Speaker
Well, I'm glad you're filming this. Perfect. Nice. Nice. Okay. Okay. I kind of like that because also that's where some of the coolest insights happen is when you just got a large population all obsessing over data and they all look at it different ways and sort it different ways. That's when little, you know, anomalies emerge and you've got really cool insights. So maybe part of democracy as well is just having a huge distributed population that are obsessed with data and that could, that could, that's some power as well, you know. And actually there's more and more emerging of the social the social science and data science. Let's see, this is like one of the hottest interdisciplinary areas where a lot of this, especially jam entering work is happening. And it's really exciting, really cool stuff.
The Role of Machine Learning in Voting
00:30:34
Speaker
Nice. Nice. Very cool. Very cool.
00:30:36
Speaker
um And again, one of the things that we've talked about doing with with the Breaking Math podcast is because there's so many peripheral topics, but you can jump from one topic to another because they complement each other and like one topic can inform rules and a different topic. it's it's It's fun. You just talked about ah data science and you talked about political science or collecting data. One of the topics that we often talk about is machine learning. um I can think of you know adversarial reasons why you'd want to or why one might implement machine learning, but I was curious if you have any applications for either voting or democracy or data science that are unique in machine learning learning that you'd like to talk about.
00:31:09
Speaker
germany There are all these germany groups who do this markup chain ensembles where they generate millions and millions of maps and with certain properties and they compare the given math the math in question to that and this has been a really an amazing success of of data science as intersects with probability theory and geometry et etc and now you see mathematicians you know testifying in courts writing amicus briefs for the for the all these germany cases so that is a place where really you know I pointed to always to see where we're how how successful you can be when you combine data science, mathematical expertise, and you come out of your ivory tower office, and you engage with the world a little bit, and you talk to like political scientists and lawyers and you know litigators and legislators, etc. Lots of good stuff can happen here.
00:32:00
Speaker
Now, how does gerrymandering actually undermine some of our democratic principles? and You know, we're taking the geometry of the area, the population of the area. Talk about how that's kind of manipulated for data. Right. So the basic and basic purpose of gerrymandering is to create districts that are preordained in some way that where one party or the other is guaranteed to win. Right, so by splitting the population or carefully carving out the population in certain ways, you can you can guarantee that your candidate will win in a certain number of districts. Which makes the districts uncompetitive, right? You know that your candidate is going to win there. Which means that all the people living there of the other party feel completely disenfranchised. They feel like their vote doesn't matter and it doesn't matter.
00:32:57
Speaker
So about 90% of our congressional districts are not competitive at all. ah They protect the incumbent, first of all. right So the incumbent has no incentive to move their politics ah around at all. They pander to the base, who's going to show up and vote in the district, which again, if they show up and vote, that's it. This person wins because the cause of gerrymandering. ah So you have this cushy 30, 40 year old family job. The only thing cushier than it is like tenure at a university.
00:33:37
Speaker
yeah well It's really hard to kick people out. Yep. You need to retire. Exactly. It's the only way. It's the only way you get new but you know politicians and new representatives and our legislatures into someone retires. Again, because I mean, there's other factors like an incumbent has more resources, name recognition, et cetera, media coverage and all that. But German is one of the main reasons why incumbents are protected. So millions and millions of people, because
00:34:13
Speaker
because districts have been jam injured into kind of like pre-ordained results, feel like they're completely disenfranchised, that they do not have any say in the political process, and this is completely true. So this is why this has been identified as one of the biggest threats to democracy. So there's kind of a list of things that we're doing mathematically wrong, like rank choice voting we should be using, primaries, you know, the political primaries are a mathematical dumpster fire of absolutely on representative democratic processes. And then gerrymandering, districting, electoral college, all of these all of these things. Math says you're doing it poorly, you need to do differently.
00:35:00
Speaker
That's one of those things where, once we identify the problem, where my brain goes is okay. You know, the problem is well known. The problem is identified what efforts are being made to correct it. And how optimistic can we be that we will be able to correct it? Because I know that people who benefit from that system are going to hang on to it very, very tightly. And I realize again, we're leaping from math topic to other topic, but I still have to ask because, you know, that's, I'm addressing the optimism and the pessimism within myself. Absolutely. the ah Politicians themselves have no incentive of changing any of the infrastructures that elected them, right? So we should not hope that even though some of the some some of the politicians declared themselves in favor of say, like, you know, rank choice voting or stopping gerrymandering, etc. But there's really no true incentive coming from the top for the any of these reforms. So really, the hope is in local action.
00:35:58
Speaker
And there is a lot of that. that's that's where that's but that's I'm really vocal about this. So rank choice voting is on their efforts in every state to implement it. ah There are something like 90 municipalities that are going to have it on the ballot. It's a member, I think, ah whether to incorporate it or not. My son, who's a junior in high school and a group of his friends, are trying to bring rank choice voting to the town that we live in here in Massachusetts. Absolutely. 70-year-olds who got fired up about this, and and they're like you know they're knocking on doors of the town hall. and and you know The first time they walked in there and talked to the town clerk, I think it was, they were trying to get informed about how how to how to bring something to the vote of the select board of the town. What the process was?
00:36:50
Speaker
And the person there's like, oh yeah, what do you guys want to do? And they're like, well, we'd like to do ranked choice voting. And she said, oh, I don't like it. You get to vote twice. Right, so this is like classic not understanding what the process is and if she just took two minutes or was able, you know, these kids could have explained to her two minutes that this is not really a nobody twice and just ranking the candidate, right, and your vote kind of contributes to the process in an iterative process.
00:37:23
Speaker
she would have been probably converted to rank choice voting. right So this is this kind of local you know but individually explaining what rank choice does, I think has a chance. And and it's you know it's happening, it's spreading. there's a The organizations who really advocate for rank choice voting say that this is the largest nonpartisan electoral reform happening right now. The US and I sort of believe it. Nice, nice, interesting. Man, my mind is still stuck on what we said earlier about data is beautiful and about empowering individuals. And I keep thinking about people that seem like they're in a hopeless situation, how much data could be collected by a bunch of people and how that might show up changing some of these, what we think of right now as harder problems. And I'm sorry, I know that that may seem tangential, but I find that sometimes I have thinking happening in the back of my head and then it blossoms into something, you know what I mean?
00:38:22
Speaker
i'm going to come back to that issue later on you know but can i just can i just ri of one word that you said yes and empowerment empowerment is a keyword keyword because once a person understands the algorithm, the mathematics behind any of these things, once they have understood really how electoral college is detrimental to like the one person, one vote, tenet, or how it skews the powers of voters in different states, once they understand that, from a basic mathematical point of view, they are not just converted, but empowered
00:38:56
Speaker
to to speak about these things to their friends, colleagues, families in ah in an educated and informed way. I think this is also, well, it's the power of mathematics, right? it It empowers people, understanding things, you know, breaking down these walls, these barriers that were built around ourselves because of math trauma, right? When these walls get torn down for people, they do feel empowered. Very good, very good. I might also ask as well, um since you've been in the United States, I know that we've had problems since before I was born. I don't think in our nation's history we've never not had had that problems. And this may be a bit of a pessimistic question. How have you noticed things change both for the better and and for the worst um ah in in your own time since being in the u United States?
00:39:48
Speaker
um Well, There are overall, I i feel like a certain groups that have felt discriminated against or or less powerful than others um have, have, how to say this, I think we are overall more tolerant, I think, as ah as a society. It may not seem like this, but I think the long view, the the birds are viewed that we are better at acknowledging our differences. Now, I say that at the time of the most the greatest political polarization, right but but I feel that's political ah and cultural. As an immigrant, I feel like things have gotten
00:40:37
Speaker
maybe a little better for immigrants maybe maybe i have a skewed view from you know like massachusetts right i think we do we are blessed being in massachusetts in comparison to other parts of the country right it could be but but there are there you know overall uh um i don't know an lgbtq person can find a place in this country yeah you know i I hope, I'd like to think, in an in ah in an easier way than they could have 30 years ago or something. or This is the kind of overall direction of more tolerance that I think we're moving in. So again, maybe not in the entire country, but there there are places in the country where that's happening. Of course, all the bad stuff is still rampant.
00:41:31
Speaker
ah and flares up every once in a while. we're we're not We're not over our political, ideological, and cultural divisions. But I feel like there was a good trend, maybe up until seven or eight years ago. In fact, when with the election of 2016, that was the first time that I felt like an immigrant on that 11 p.m. on the day of the election. I was suddenly aware in a new way of my name, my weird name, my little accent on the letter C at the end, of of my accent when I speak, even of the fact that my passport, which is a US family, US s citizen, but it says place of birth, Bosnia and Herzegovina, even that kind of had some sort of a new new meaning carried a different way for me. So this is the bad part, right? I felt like things were going
00:42:30
Speaker
fairly well up until seven or eight years ago and there's there's a lot of backsliding ah happening now so I'm not it's not a satisfactory answer but yeah and I think in in in fairness my answer was such a wide sweeping answer like how do you even answer that but you know still I just I just ask for perspective yes of course I completely understand that and can see that firsthand um with the shift in cultural societies. um but My dad's an immigrant as well. so i see The name is just as actually longer and much more complicated.
00:43:12
Speaker
yeah even Even though I have a but much more um Americanized name. that's so yeah with that like just Just a topic shift a little bit. um If we're going to processes within our legislative system, think about apportionment, right? So how how are we looking at like legislative seats? um how is this like historically all the way to like now current day how is this shifting um looking at that over the past i don't know 250 years that but there's there's really an interesting story behind us so there's there are two two things i could say that one is
00:44:06
Speaker
um The House of Representatives, it says so the the but congressional led legislative, the the federal legislative system, right? So our House has 435 seats. And, you know, typically you don't stop and ask, why 435? Where'd that come from? It turns out that has a real interesting story. And 435 is a terrible number. that should it should it should be our house should be about 700 representatives um large. Now, this is not a popular opinion, right? You don't go out in the street and say, you know, I want to increase the number of politicians in Washington back then, so the person in the street is not going to like that. But it turns out our house is too small.
00:44:48
Speaker
right? Each representative represents about 760,000 people. That's impossible to effectively have a constituency that's that large. You cannot have your finger on the pulse of your of your of the people you're supposedly representing when there are so many of them. So this is one issue that yeah and the the founders identified 50 years ago. Madison in particular was very outspoken on this and he
Legislative Representation Challenges
00:45:17
Speaker
said, you know what, each representative should represent about 30 to 50,000 people.
00:45:22
Speaker
So $30,000 to $50,000? I remember $760,000 that I just said. nothing Yeah. So $50,000 is unfeasible now, but something you know less than $760,000 should happen. So the house was frozen at $435,000. in the 1920s because of the politics of the time, because of anti-immigrant and racist policies of the time. I don't want to get into that sort of a sidebar. yeah And I talk about talk about that in in my books. But it was it's it's an artifact of that moment that happened 100 years ago. It makes no sense right now that we are still at 435. So that's one
00:46:09
Speaker
mathematical ah issue. The other one is how do you apportion the 435 seats to the states after every decennial census, so um and there's a formula that does that. And that formula has an interesting story. It's been disputed and changed a dozen times over the course of of our history, and it's not the best possible formula. ah The formula that we use now actually favors small states. It tends to award small states more representative. And there's a better formula that we should be using that's a little more optimal in that way. It doesn't favor large versus small states. it It tries to kind of be as objective as possible. So then really interesting math story behind all that as well.
00:46:54
Speaker
So yeah, you wouldn't think there's any math. You're thinking about representatives, House of Representatives. There's always math. yeah But there's always math. There's always math. that and right So I'm telling the story about our house our Congress, right but all of this trans maps onto state legislature as well, right states of district, state allocated representatives, et cetera. So ah the the everything that that I've said applies to the to those but state level ah allocation. OK. Nice. So of course, there's a lot you you brought up there. And the question i'm not I'm not going to go into right now would be, of course, you know what can we do to improve it? Because that is always an ongoing question. But obviously, being aware of it is very important as a start. So perhaps you know a legal podcast, maybe Breaking Law. Would that be a good podcast name? Oh, Breaking Law. Come on. It's got Someone else has to start the Breaking Law, you know derivative of breaking math. But you know OK.
00:47:54
Speaker
They can go into that and yeah yeah you know but about how to actually change it or how to fix it. We know that the book focuses on a lot of the mathematical theories, but we also want to look at like practical implications of implementing that. So what are some of like the legal and constitutional hurdles that we're going to come up against with our voting system? Right, i so I'm trying to paint that picture as well, although I'm certainly not an expert in it, but it felt like the book would be complete if I just presented the math without without addressing the real the real life issues with with their implementation. So it depends on which
00:48:33
Speaker
ah issue you we were talking about. So for example, with any anyium local so for example if voting and elections are completely left up to the purview of the states, right? So a state decides completely how they're going to run elections. So that's a state level decision. and So each state could do their own thing. Where, for example, if you talk about the Electoral College, that's something that, oh, and by the way, voting, there's nothing in the Constitution that says anything about voting, right? Again, states are in charge, and there's no guarantee in the Constitution that people will
00:49:13
Speaker
vote and that it's up to people to elect anything, right? In fact, when we vote for president, we are not voting for president. We are voting to advise our electors from our state on how they might, should they choose to vote for the president. And happening in a constitution that terms that gives the right to vote to us as citizens. That's completely left to the states. And a and in the in the ah in the case of the presidential elections, it leaves it up to the electoral college.
00:49:50
Speaker
If we are talking about the electoral college, that is in the Constitution, so so that would require an amendment to say eliminate, and that would that would be pretty much impossible to do because you need three, four of the states to ratify an amendment, and that would never happen because electoral college gives smaller states some agency and and and power that they would be loath to you know relinquish. ah There are others, so for example, you could, one of the problems ah with our democracy, that we have a single member district, so each district, elects one representative, either to the state legislature or or the House of Representatives. Most other democracies in the world have multi-member districts, so a district elects more than one person, typically three, five, or something like that. Now there's a federal law that says all all districts
00:50:43
Speaker
congressional districts have to be single-member districts because of some bad things that had happened in the past. a Again, bad math. We could fix all that with good math. And that would require, if we wanted to eliminate single-member districts from federal elections, ah we would have to... um What's the word? um repeal that law. So that's ah that yeah that would be an act of Congress that that that could happen there, right? So there are various levels of hurdles here, right? State level, Congress level, and sort of a constitutional level hurdle, depending on what what issue you're you're talking about. So it's just like this giant mess, basically.
Empowering Citizens through Democratic Mathematics
00:51:29
Speaker
um Now, if we're just diving in thinking about like larger scale, people that want to make change, people that want to have advocacy for making change. When you're thinking about implementing this in our education system, um how how do we start that? What are the good resources that we can pull out of here? Or where would we find additional resources beyond the book? So that it's almost like I claim to this question because I because i get to advertise my own work work with that. A of colleagues of mine and I run what's called the Institute for Math and Democracy. yeah And we do lots of research and education work and outreach. And the educational work in particular, ah ah there are specifically as a page,
00:52:24
Speaker
on our on our web page that gathers all kinds of resources and materials for teaching this stuff, math and politics stuff, yeah and various levels. There are materials for middle school teachers, high school teachers, and and and college college college faculty as well. And there are materials, so this is actually ah important. One of the hurdles with with teaching mathematics that's kind of democracy-minded is that ah a lot of teachers in schools are constrained by their like state or or or or school district requirements or what they have to cover. And you know a lot of the teachers feel like their hands are tied and they they don't really have any wiggle room in in the curriculum, et cetera. So that's a real problem. And then you have to map everything everything that they do. They have to map to these common core standards or some kind of state.
00:53:13
Speaker
requirements for or achieving certain outcomes, et cetera. So what we also do, because we have lots of little sort of modular modules of old units that can be plugged into existing existing curriculum. So you don't have to teach an entire class of mathematics, right? Where a few people have room to do this. I'm lucky, I teach one of those classes and I'm so lucky that my you know place where I work is letting me do that and my colleagues in the math department are happy for me to do it, but I realized I thought everybody's set up. so so there So there are these modular ways that you can try to plug plug stuff into into education. What I think is really crucial is that we start doing this in an interdisciplinary way. right Obviously, someone teaching
00:53:58
Speaker
You know, US government in high school and mathematics read this is something that straddles these two, these two areas so it would be wonderful in some ideal world, but this kind of joint effort to bridge to bring to sort of introduce these topics in in both classes. Like ah my son's taking APS history, they're talking about electoral college, but they're not talking about the math of electoral college. They're not analyzing how it plays out against the popular vote mathematically. So that's something that a math teacher might somehow bring.
00:54:35
Speaker
a perspective on. but so So there's lots of opportunity for collaboration, interdisciplinarity, and and we have we have a lot of resources on on this Institute for Math and Democracy a we website. There are lots of books also at this point that can be used as textbooks. I'm hoping my book will become a resource work for teachers as well. So yeah, any of the listeners who want to learn more about this should Google Institute for Math and Democracy. They'll find my name and my email attached to it as well. They should write to me. I'm always happy when i when I get emails from people who want to get engaged in this sort of education direction.
00:55:12
Speaker
I did want to ask you um real quick. um So during this podcast, of course, we talked about your book, Making Democracy Count. And there's a ton of stuff in this book. But as a math enthusiast in general, I had a couple of questions about what are your what are you most passionate about in mathematics and what other general topics that might broach not only mathematics, but other areas in general. What are your favorite things to learn about and teach about?
00:55:40
Speaker
Well, certainly this has been my my the main feature of my teaching and research last last few years, but I do love my topology. I'm a topologist and I do ah the you know algebraic topology and I've written papers and books on the topic, so I haven't abandoned that. It's just a little bit of a hiatus, but that's that's really my sort of ah kind of kind of research, research passion. ah And I have been able to bridge this gap between math and politics research and topology research. I'm kind of getting the best of best of all worlds. So I'm very i'm very excited with the place. I mean, you might call it a kind of midlife professional crisis, right? That I sort of switched seven, eight years ago to do something else. But I just kind of, but you know, I would so i was called to this.
00:56:28
Speaker
And it's been really fantastic that that's a crime. So there is a bunch of stuff that I would like to learn that has to do with data science. where I feel like i could I could contribute even more in this direction of of of math and politics. So, you know, I mentioned like Python. I just know that word exists, but I don't know anything else. I like coding and just just general but of statistics. I have no statistics skills, so I'm really excited about learning that. And i' also on the other side, sorry, now you've got me going.
00:57:07
Speaker
um I would love to learn more political science. I'm also realizing that I don't know any. Everything I know I put in this book, and I hope that it's correct. People have checked it. They could call you to explain a concept at a certain level. You really have to understand it at a much higher level. right so I feel like I'm okay with that on the mass part of the book, but political science and like the the issues of of the judicial system and all that, it's bi everything I know is basically in there. So I'd like to learn more, to be able to kind of understand it, internalize it at at at sort of a next next level. I feel like I could be more
00:57:52
Speaker
I could, ah there could be more collaborations with people who come from those worlds, you know, I was just talking to someone who teaches at the Harvard Law School yesterday, and we find all this common ground that we could cover. ah But I wish I knew more about that type of thing. like they i could I could contribute a lot more. So yeah, political science is a power, power, collaboration, game theory. I would like to learn more about it. Sorry, I'm even trying to say it. Don't apologize. So the things that you want to learn are some of my favorite topics.
00:58:31
Speaker
Right. Cool. Awesome. awesome Yeah. No, this whole episode has been phenomenal. Everything you said, I'm hoping that this podcast can inspire other more qualified people that, you know, than us to have conversations with you and with others about democracy and data science and politics. So hopefully there'll be a follow up with some others, you know? I hope i hope so too. And I would add to the fact that. There is math and democracy. i mean This is like the the first thing of people are like, what's math and democracy? why Why are you putting those two words together? They don't belong together, but they belong together in and in a really cool way.
00:59:09
Speaker
that can be relevant. It's obviously timely, right? It can be a way for us to get past the emotion and politics and partisanship. We can, re we can retrieve to the formalism and again, detachment. That's where it comes up. I like to say that and it's not, you know, it was not good to be detached, but in this case, I think we should be. And math is providing us the framework which do to talk this dispassionately and apolitically and and in a nonpartisan way about some of these basic tenets, basic processes of democracy. If there is one big thing that you want anybody to take away from this today, from the conversation about your book in general, ah what is it?
00:59:58
Speaker
ah yeah You you know educate yourself about you know the mathematical quantitative underpinnings of democracy. there's There's a lot there and to be an effective citizen, effective participant in democracy, I feel it's imperative that you know how the quantitative aspects of this work. Wonderful. excellentence Excellent. awesome and then if If anyone has questions, um what is your social media handles? I thought you were going to say, what is your social security number? No, no. No. Sorry. No, just kidding. No, social media handles. Where can we find you online or? You know, I am on, I am on Facebook and Twitter and LinkedIn. And if you just put in a smart voltage, I come up. I have a, actually, Google says I'm the only person on the planet with this name, so.
01:00:59
Speaker
i Cool. That is cool. Yeah, you and me both actually have yet to meet another Gabrielle Hesh actually and I've i've looked so i really yeah interesting cool i I found out there is somebody with the same name as me. um She's probably three years older and also has higher education degrees lives within probably 30 minutes of me. Oh, no.
01:01:28
Speaker
go away from the planet yep so that that's mean There's a plot. There's a plot of some like plot twist. raking what o raking i what Wow. Yep. So I am not the only one.
01:01:50
Speaker
fair enough but So in any case I would like to thank you for coming on the show today and it was a pleasure having you.