# Mathematical Fairness in a Constitutional Convention

This is a guest post from Sarah Fisher, Assistant Professor of Political Science at Emory & Henry College and Rachel Bayless, Assistant Professor of Mathematics at Agnes Scott College.

As a political scientist and a mathematician we come from seemingly disparate fields- and what often are in an academic setting (quantitative political science notwithstanding). This summer, we had the opportunity to highlight the interconnectedness of these subjects and engage students in a collaborative activity.

We were each teaching a course during an intensive three week program for gifted middle school students. One course focused on political simulations and problem solving in international affairs (taught by Sarah), while the other course was concerned with mathematical problem solving (taught by Rachel). As part of the international affairs course, students constructed a constitution for a newly formed fictional country (more information on this simulation can be found on Florian Justwan or Sarah Fisher’s website). The international affairs students acted as delegates for a constitutional convention. Meanwhile, the mathematics students learned four rigorous definitions of fairness and applied that knowledge to different types of voting systems. We brought our students together to decide which voting system would be most appropriate and “fair” for the new fictional country.

The international affairs students were divided into different societal groups with preferences that would likely favor one type of voting system over another. For example the societal group with the largest population would prefer a plurality voting system because their candidate is likely to have the highest number of first-place votes. On the other hand, a small societal group may support using Borda count because even if their candidate doesn’t have the most first-place votes, he/she can still win the election if they are ranked second or third by many voters.

We collaborated with several goals in mind. For the international affairs students, a primary goal was to utilize mathematical arguments to solve a societal problem. Applying the formal definition of fairness to electoral systems showed that there is no “perfectly fair” voting system. Rather, politicians must make tradeoffs between ideals of fairness, societal preferences, and personal gain. During the simulation, the lack of a clear “right” or “wrong,” even in a mathematical sense, was frustrating and illustrative. As a class, students settled on using the Borda count method in their elections.

One of the primary goals for the mathematics students was to identify the connections between mathematics and social justice. Mathematics is not just a tool for science, engineering, or statistics. Mathematics can help inform ethical issues ranging from a fair election to a fair way to distribute organs for organ transplants. Both sets of students had the chance to teach one another what they had just learned and needed to listen to classmates who were the “experts” in a given area- either constitutional design or mathematics.

The mathematics students were provided information on each of the fictional ethnic groups and instructed to act as consultants for the constitutional convention delegates. We spent an entire six hour class day on this simulation, but this same goal could be achieved using an online platform or a shorter amount of dedicated class time with undergraduates.

The activity’s success encouraged the instructors to seek out more ways to collaborate in the upcoming semester. What ways could we incorporate other fields of study into our classrooms?