Math 150: “Voting and Elections: A Mathematical Perspective”—Tanya Leise, associate professor of mathematics.

The ideal voting system, one might suppose, would be a system that’s easy to understand and implement, in which every ballot counts equally and everyone is motivated to vote to express honest preferences.

“There’s no such system,” says Tanya Leise, associate professor of mathematics. “All the different systems have their drawbacks.” But that’s where things get interesting—and that’s why she designed this new course, in which students examine voting systems in terms of both numerical workings and sociopolitical ramifications.

Consider plurality voting, in which the winner is simply the candidate who receives more votes than any other. If there are three (or more) candidates, this system can result in a winner that the majority of voters don’t want. And if candidates A and B are nearly tied in the polls leading up to the election and C lags far behind, voters who hate A might vote for B even if they most prefer C, because only B seems to have a chance to beat A.

In fall 2016, Leise’s students—many of them non-math majors—proved theorems and worked through example cases to demonstrate mathematically how these problems, and others, can occur. They debated the relative merits of plurality voting, approval voting  (in which each voter can endorse any number of candidates) and instant-runoff voting (in which each voter ranks the candidates in order of preference). They read academic journal articles, as well as news about elections around the world.

Each student also chose a real-life voting or scoring system and, as a final project, analyzed its strengths and weaknesses and proposed improvements. One student suggested a way to break ties in NESCAC football championship rankings. Others addressed voting for the Emmys, Grammys and Oscars. A student from Greece presented ideas for his homeland’s elections, saying, “It’s important to have a good democracy in the country that invented it.”

After Nov. 8, the class studied how the Electoral College gives some states’ voters more power than others’. They also discussed the influences of pre-election polling and the Supreme Court’s striking down of parts of the Voting Rights Act. Several students did final projects on the American electoral system, Leise says, “but they each have very different ideas about how they would reform it.”