By Ismar Volić
Every time I teach my Math and Politics class at Wellesley College, I run a little poll near the beginning of the semester: Suppose the world was down to two kinds of pizza—pepperoni or veggie, which would the students choose? After some grumbling about exactly why those two, the show of hands always ends up being close; the tally was 13-12 in favor of pepperoni the last time I taught the class. So we agree that pepperoni is what we would order for everyone if we had to choose just one. So far so good.
Then I ask the same question, now with barbecue chicken as the third option. After some more grumbling, the new vote invariably turns out interesting because of the decent number of defectors. In that same class, pepperoni received 10 votes, barbecue chicken 8, and veggie 7. So we declare pepperoni the winner yet again and the students agree that this is what the whole class would eat.
But then comes my favorite part. I say “OK, pepperoni it is…” and pause. There are few moments more awkward than a silent classroom, and the students quickly realize that something is up. I can see the gears churning, eyes widening, and then finally someone says “But wait, most of us don’t want pepperoni!” And so it begins…
I started teaching Math and Politics three years ago as a short summer course for high school students. I’d always had an interest in how mathematics interacts with the society and, after teaching a Cryptography and Privacy class a few years earlier, I thought I’d offer Math and Politics mostly as a way to learn some more cool stuff about the interaction of the two (dirty little not-so-secret: when we college professors want to learn about something, we teach a class on it). The short course was a lot of fun, but the most striking feature was that the topics we covered—basic voting theory, Electoral College, and gerrymandering—were completely unfamiliar to the students. There was nothing in their education so far, in any of the eleven states they came from, that even indicated a brush with political quantitative literacy.
At the same time, the students absolutely loved the class. They found the material immensely engaging but, more importantly, they got angry that nobody ever told them about this stuff. Why hadn’t they been told that so many basic processes that run our democracy were so deeply mathematically flawed? They sighed and shook their heads when I talked about plurality voting as a mathematical monstrosity, the difference between the popular and electoral votes, the rounding issues of the apportionment process, or the geometry of gerrymandering and the blatant racism as its outcome.
After that summer class, I decided to go full on with Math and Politics. With support from my colleagues, I introduced it into the math department curriculum and have taught it several times since. The topics we cover are voting methods (with the pizza example as a segue to the discussion of the many defects of plurality), both ranked and cardinal, proportional representation, the basics of social choice theory, Arrow’s Theorem and related results such as the Gibbard-Satterthwaite Theorem, a bit of game theory, apportionment and the Balinski-Young Theorem, Electoral College, math of districting and gerrymandering, weighted voting, quantification of power, Banzhaf and Shapley-Shubik indices, and the abuse of statistics in politics.
A nice feature of the class is that there is a narrative we follow. As it turns out, all the topics listed above can be visited by tracing the journey of a ballot in presidential elections from the moment it is cast to the inauguration on January 20th. The question of how the states decide the winner leads into discussion of voting and social choice theory, the number of electors in a state serves as an intro to apportionment, and the Electoral College, while of course being an interesting mathematical topic unto itself, brings us to the study of weighted voting and the quantification of power. As delightful as it is, from the pedagogy point of view, to have such a story as the backbone for the class, it is in the end disconcerting that so many of the mathematical flaws of our democracy are on display in this fundamental democratic exercise of electing the next President of the United States.
The class runs as a combination of lecture, discussion and group work. The students turn in math homework but also have to think about related “big picture” questions and participate in discussion. I love lighting the fuse on passionate exchanges by asking the students to try to advocate for their favorite voting method, or discuss the academic versus practical importance of Arrow’s Theorem, or whether and how the Electoral College should be abolished or bypassed. Several classes are dedicated to group work on fun topics like voting in Eurovision, the Oscars, Survivor, ATP tennis rankings, and the Heinemann Trophy; figuring out how the 2016 presidential elections would have turned out had a different apportionment method been used; and playing around with gerrymandering.
The inherent interdisciplinary of Math and Politics also draws a wide array of majors. Among the 25 students who took the class last time it ran (25 is the cap, and the class always has a lengthy waitlist), 14 majors were represented. They included political science, history, economics, computer science, literature, peace and justice studies, and psychology. The representation of such a variety of points of view makes the discussion so captivating that I often let the conversation run far beyond the allocated time. I also love that the students frequently know much more than me about the U.S. history, economics, and political theory and are eager to share their knowledge. Additionally unusual is the consistently large percentage of students from underrepresented groups who take the class. This is refreshing, especially as our math department—as is the case in many higher education institutions throughout the country—struggles with recruiting and retaining such students.
After teaching Math and Politics a couple of times, I started to comprehend the extent of political quantitative illiteracy, or political innumeracy, that permeates our politics and education. As a result, together with colleague Stanley Chang and with Wellesley College’s support, I founded the Institute for Mathematics and Democracy (IMD), a place dedicated to education, research, and outreach in the intersection of mathematics and politics. The institute has grown immensely in the last two years and is undeniably answering a pent up demand for a place that would serve as a nexus for students, teachers, professors, researchers, and activists who care about the role of mathematics in democracy. The Math and Politics class has served as the pipeline for students to get involved with IMD, continue learning, do research, develop teaching materials, organize talks and conferences, and become advocates for mathematically sound democratic practices. Judging by our expansion rate, we have a bright and busy future ahead.
It’s a no-brainer that political quantitative literacy is good for everyone. A politically numerate population would not pass up a chance to make politics more inclusive and representative by employing better mathematics in our democratic processes. An example of such a missed opportunity is my home state of Massachusetts where a statewide implementation of ranked choice was voted down in the 2020 elections. This happened despite the well-funded “Yes on 2” campaign with essentially no counter campaign. What sank ranked choice was the campaign’s inability (that can reasonably be blamed on the pandemic) to educate enough people about its benefits. The vote against it was really a vote of confusion, of fear of something new, and the inability to break from the old.
If everyone in Massachusetts had at some point been taught about ranked choice, this initiative would have passed by a landslide, voted in by a politically numerate electorate. Education, yet again, is the key. Bringing political quantitative literacy into the curriculum at all levels—K-12 as well as college—would strengthen our democracy and make it work better for everyone. My Math and Politics class is a small step in that direction.
Ismar Volić is a professor of mathematics at Wellesley College, the Director of Institute for Mathematics and Democracy, and the President of the Bosnian-Herzegovinian American Academy of Arts and Sciences. Ismar is a Rank the Vote advisory board member.
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