Mathematics of Voting Class Proves Enlightening

As Harvey Mudd community members gather across campus to discuss election results and to process their feelings about them, we found one group of students who share a unique perspective on the outcome, due in part to their participation in Professor Michael Orrison’s Mathematics of Voting class. One of their takeaways: how you vote may matter more than what you think of the choices.

“Voting is definitely not as simple as everyone thinks it is. Just learning about basic voting systems took up an entire quarter!” says Alex Chang, one of eight first years in the class.

Students spent the half-semester course examining various voting systems and comparing outcomes based on how the votes were tallied.

They also did individual research projects and made presentations on topics ranging from attempting to find a more efficient alternative to Robert’s Rules of Order to rating voting systems based on how happy voters are with the outcomes.

In the process, they learned not only how to think locally and globally, they also learned about the effect of voting systems.

“It’s important for students to realize that mathematics is powerful and it can put you in a position where you can see problems more clearly than ever before. But let’s remember: there are people involved,” says Orrison, professor of mathematics.

The class explored ways in which voting systems can be manipulated when voters vote disingenuously. Say a department is hosting a dinner and asks faculty to rank the drink choices— wine, beer or milk—by giving each choice three, two or one points, depending on their preference. If someone likes alcohol and prefers wine but many in the group prefer beer, then that person might put wine first, milk second and beer third in hopes of diluting the beer vote.

The same could be said for third-party candidates in a national election, for example. Someone who prefers the Green Party or Libertarian candidate might vote for a major party candidate because they want their vote to count.

Ian Taylor ’20 ran a simulation for his presentation in which he found that 11 percent of the time disingenuous voters benefited by not voting for the selection or candidate that they preferred.

Orrison is quick to point out that the class is not intended to teach students how to manipulate elections. He wants to raise their awareness so if faced with a voting situation, they can educate others by pointing out the pitfalls of any election procedure.

Orrison first got interested in voting systems as a graduate student at Dartmouth College researching ways to analyze rank data. He read some papers suggesting that certain techniques could to applied to voting questions.

“Many authors were saying you could do it but few people were using the mathematics I was interested in—symmetry and fast algorithms—to look at voting,” Orrison says.

When he first arrived at Harvey Mudd College in 2001, Orrison wanted to get students involved in the kinds of research he was interested in. Voting was a natural starting point because almost everyone has participated in voting affecting the nation, the college or their own dorm.

Over the years, voting issues were not only an entry point to his research but voting questions became more and more intriguing, and his research began to shift toward voting.

“With a class like this, I feel like I can balance the kinds of questions that might seem purely mathematical with questions around voting and decision-making that seem undeniably applicable,” Orison says.

At the beginning of his research, Orrison encountered many voting systems and found a couple that he liked because they were mathematically interesting and impervious to typical attacks or criticisms.

Today, he’s reluctant to recommend any specific voting system.

“What I’ve learned since then is that no matter how mathematically amazing a voting system is, if everyone in the organization is suspicious that the voting system can be rigged or they’re not willing to trust the result because the system is too complicated or unfamiliar, you can do more damage than good,” Orrison says.