Why Mathematicians Love Ranked Choice Voting

The Institute for Mathematics and Democracy (IMD) has released what may be the most comprehensive empirical study of ranked choice voting ever conducted. The 66-page report analyzes nearly 4,000 real-world ranked ballot elections, including some 2,000 political elections, and more than 60 million simulated ones to test how different voting methods perform.

The study’s conclusion is clear. Ranked choice voting methods outperform traditional first-past-the-post elections on nearly every measure of democratic fairness.

IMD’s research team, led by mathematicians from Wellesley College, William Jewell College, Colby College, High Point University, and Boston University, found that IRV and Condorcet methods of tabulation consistently produce outcomes that better reflect the majority will and reduce the effects of vote splitting and “spoiler” candidates.

“The best performing methods are IRV and Condorcet,” the report concludes. “They are least likely to be susceptible to spoiler effects, are mostly resistant to strategic voting, and are unlikely to elect weak or fringe candidates.”

Mathematics for Democracy

Founded in 2019, the Institute for Mathematics and Democracy brings together academics, educators, and civic leaders around a single mission: to use mathematics as a force for democratic renewal.

Ismar Volic, the institute’s director, said the study reflects that mission in action.

“We need better electoral engineering, namely a better design of mechanisms of democracy that would produce outcomes that are favorable to more people,” he said.

At its core, the Institute believes that mathematical literacy is civic literacy, and that understanding how votes are counted is just as essential as casting them.

The Evidence Behind Reform

IMD’s latest research analyzed ranked-choice data from Australia, Scotland, and the United States, alongside simulated models based on tens of millions of hypothetical ballots. Across both real and simulated elections, IRV and Condorcet methods agreed on the winning candidate in an overwhelming majority of cases.

Plurality voting, the system used in most U.S. elections, performed the worst. It regularly rewarded polarizing candidates and encouraged strategic “lesser of two evils” voting.

Ranked systems, on the other hand, gave voters the freedom to express their full preferences without fear of wasting a vote and encourage moderation, since candidates must appeal beyond their base to earn second-choice rankings.

While IRV earned praise for its simplicity and real-world adoption, Condorcet stood out in the data as the most mathematically fair system. Condorcet methods were found to be “the most resistant to the spoiler effect” and to produce the most broadly supported winners.

The report notes that Condorcet elections were the best at avoiding “fringe” or extreme candidates. This is because Condorcet elections avoid a “center squeeze” in which a candidate preferred by a majority of voters when considered head-to-head against either a candidate on the left or a candidate on the right cannot prevail.

From Theory to Practice

The IMD’s work connects with a growing academic interest in how mathematics can inform public policy. Among those bridging that gap is Nobel Laureate Eric Maskin, who spoke at the Institute’s recent conference on mathematics and democracy held at Wellesley College in Massachusetts.

Maskin, a pioneer in the field of mechanism design, studies how institutions can be structured to achieve socially desirable outcomes.

“Mechanism design is centered around the goals that society wants to attain,” he explained. “The idea is to try to figure out a mechanism or an institution or a procedure that will attain those goals.”

In his presentation, Maskin highlighted the same flaw that IMD’s study quantifies: First-past-the-post elections too often produce winners that most voters actually oppose. He advocated for Condorcet-style voting, in which voters rank candidates, and the winner is the one who would defeat all others in head-to-head matchups.

He also spoke about the challenge of translating technical research for a broader audience.

“It’s actually much harder to write for a general audience,” he said. “They’re not going to understand the language that professionals use. I have to think about every word, and I don’t want to oversimplify.”

That commitment to clarity mirrors the Institute’s philosophy. For IMD, reform depends as much on education as on analysis. The organization focuses on teaching citizens how to evaluate claims about fairness, data, and democracy.

“Most ideas for reform, if you trace them back, go back to an academic,” Maskin said. “But it can’t end with academics. There’s also the very practical problem: how do you get these changes adopted?”

The Path Forward

Maskin pointed to ranked-choice voting initiatives in Maine, Alaska, New York City, and San Francisco as examples of progress made possible by education.

“In order for the public to be willing to vote for change,” he said, “they have to be educated. They have to understand why the current system is flawed and why the new proposal is better.”

That is precisely the Institute’s mission: to make democracy not just fairer, but smarter.

Through its research, teaching, and outreach, the mathematicians at IMD are helping citizens see elections the way mathematicians do, not as static contests but as underlying systems that can be designed, tested, and improved.

If democracy is a design problem, perhaps it is time to let the mathematicians help solve it.

Why Mathematicians Love Ranked Choice Voting was originally published by Independent Voter News and is republished with permission.