This article presents a project that is meant to deepen student understanding of what it would mean for one preference voting method to be "better" than another. In the project we show the students how to rigorously compare the methods of plurality and plurality with elimination, and we then allow them to compare two other voting methods of their choice. The primary way that we evaluate voting methods is by analyzing how frequently different methods fail various fairness criteria. This project is particularly relevant since the state of Maine voted in 2016 to use plurality with elimination as the voting method for many of its elections.