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math_class_smWhy not examine democratic electoral systems from a mathematical perspective, math faculty member Matt Simonson thought, leading up to the presidential election. Together with colleagues Becky McCormick and Juan Ramos, Matt developed a unit for their Algebra II Honors students.

“We compared voting in the United States to voting processes in other democracies like Germany, Japan and Israel,” says Matt. “We looked at the advantages and the flaws in our system, and how it compares to other countries that use proportional representation; for instance, if a party receives ten percent of the vote, that party gets ten percent of the seats.”

The students also studied how different systems apportion decision-making seats—how seats are divided among different states or parties. For example, if a state qualifies for 2.5 seats in a government body, based on the population, should two people or three people get seats? Or, if three parties are competing for 100 seats, one party gets 33.3 percent, one gets 33.3 percent, and the other gets 33.4 percent: If the numbers round down and there is an extra seat, which party can own it?

Students analyzed historical cases and hypothetical cases. They looked at different ways to count votes: Should voters rank their choices? Should run-off elections be part of the system? They investigated more mundane examples of voting, such as sportswriters’ voting for the MVP, or the way a team votes for a captain. Matt says they hope to make the election math unit an annual exercise, even in years without a major election.

“The math is rich and the lessons are important,” says Matt. “This is a great opportunity to connect with students whose interest lay in other disciplines, such as economics, history and political science, and show how that topic can be understood in mathematical ways.”