Solving Democracy’s Flaws with Logic and Precision
Ismar Volić discusses how mathematics can improve voting systems, prevent gerrymandering, and address Electoral College flaws. His insights highlight the power of numbers in making democracy fairer and more representative.
Ismar Volić is a scholar of remarkable breadth, whose work bridges the worlds of mathematics and democratic integrity with unparalleled clarity. As a Professor of Mathematics and the Director of the Institute for Mathematics and Democracy at Wellesley College, he has dedicated his career to exploring how mathematical principles can enhance the very foundation of governance. His book, Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation, is a groundbreaking examination of how mathematical insight can expose flaws in electoral systems and offer tangible solutions to some of democracy’s most pressing challenges.
A leading voice in the intersection of mathematics and social choice theory, Volić’s contributions extend beyond academia. His writings in The Hill, TIME, and LitHub demonstrate a rare ability to translate complex mathematical ideas into compelling narratives accessible to the public. His lectures—delivered across twenty countries—reflect both the global significance of his work and his unwavering commitment to making mathematics a tool for democratic reform.
In this exclusive interview with Reader’s House, Volić shares his motivations, insights, and vision for a more mathematically sound democracy. From voting systems to gerrymandering, from the Electoral College to electoral fairness, his work challenges us to rethink the very structures that shape political representation. His perspective is not just illuminating—it is essential for anyone who believes in the power of numbers to safeguard the principles of democracy.
Ismar Volić is a visionary scholar whose groundbreaking work unites mathematics and democracy, offering profound insights into electoral fairness and representation.
What motivated you to explore the intersection of mathematics and democracy in your book, Making Democracy Count?
I knew I wanted to be a mathematician from an early age, but was always also interested in the intersection of mathematics and society. This curiousity was amplified by my own personal story as an immigrant who came to the U.S. during the war in Bosnia in the early 1990s. I was witness to a breakdown of democracy in its most horrific form, and that has followed me my whole life.
Several years ago, I started teaching the class Mathematics and Politics and realized that students cared deeply about quantitative aspects of democracy – even if they are generally put off by math. By the end of the class, they declare themselves to be “math people” and are ready to do something about all the bad math we use to run our democracy. Ultimately, the book grew out of this class and is based on the material I cover in it.
How do you think mathematics can help improve the fairness of electoral systems?
Most democratic processes, like voting, districting, and allocating legislative seats, are fundamentally mathematical. Various algorithms and formulas govern how we run these mechanisms. But these processes are not unique, we have options for each of them, and math can tell us which ones are flawed and yield unrepresentative results. It can suggest better ones, those that are more sophisticated at capturing the collective preferences, desires, and needs of the voters.
What do you consider to be the most significant mathematical flaw in current voting systems?
The main culprit is probably plurality, or first-past-the-post, voting. This is the method we are all familiar with where the voter chooses one candidate and the candidate with the most votes wins. As soon as there are more than three candidates, this system becomes a mathematical atrocity. It can cause vote-splitting, it makes it harder for smaller or independent candidates to enter the political arena, if stifles diversity, and it encourages strategic voting and negative campaigning. There are many systems that avoid these problems, and they are all based on the simple idea that taking more information than just their first choice from the voter is better – math can then do more with more information, it can better capture the “will of the voters” if it has more to work with.
Could you explain how gerrymandering distorts political representation from a mathematical perspective?
Gerrymandering is a way to group the voters a certain way into districts so that the outcomes in the aggregate are unrepresentative of the total population and favor one political party. For example, Republicans in North Carolina won about 53% of the vote in the November 2024 elections, but took 10 out of 14 congressional seats, which is 71%. Gerrymandering is silencing the voices of millions of voters because it makes districts uncompetitive, with predetermined outcomes. Most races in the U.S. are not competitive because of gerrymandering, and this is terrible for democracy. Mathematicians are doing some amazing work in countering this practice and coming up with sophisticated ways to detect it and suggest better ways to draw district boundaries.
What role do you see for mathematics in overcoming the challenges posed by the Electoral College?
The Electoral College causes voters in certain states to have disproportionate power over voters in other states, it violates the “one person, one vote” dictum, and it can elect a president who did not win the popular vote. The Electoral College is unique to the U.S.; no other country in the world uses anything like it or wants anything to do with it. It is an archaic system that’s left over from the 250 year-old politics and traditions, slavery being the most offensive among them. Some people consider the Electoral College to be sacred like everything else the Framers of the U.S. Consitution set up, but this is misguided. As it turns out, they could not agree on a method to elect the president and ultimately established the Electoral College as a concession to Southern and slave-owning states. Math is clear on why this system should be abandoned and replaced by the popular vote.
How do you balance the mathematical and legal considerations when proposing reforms to electoral systems?
I don’t have to. I am a mathematician and have very limited knowledge of the legal system. My support for a particular reform is based purely on math. I see my job as providing people who are better versed in the ways of the legislature and the judiciary with the tools to advocate for those reforms. I supply the confidence that comes with the objectivity of mathematics provides but the true “in the trenches” advocacy and implementation is done by other, more skileed people. This kind of collaboration is becoming more the norm, which is fantastic. Democracy requires expertise from all over the spectrum, and experts in one area must talk to experts in the others.
What advice would you offer to other authors looking to write about complex social issues through a mathematical lens?
To go for it. Merging math and social issues is not easy because the subject is so interdisciplinary and draws from many fields, but it is also extremely interesting and engaging. Bringing quantative considerations into discussions of politics and democracy is underappreciated but absolutely necessary. Mathematics can inform better processes and give us the common ground based on its universality and detachment from politics. This increasingly elusive shared foundation is all but gone from our politics and we have to rediscover it in order to move past the gridlock.
