This session features an interdisciplinary approach to a wide range of issues related to electoral systems. Elections are recognized as cornerstones of democracy. Yet today there are increasing calls to change our electoral systems, and criticisms of past practices are attracting more and more adherents. Ideas for reform include changes not only to the information that voters are asked to enter on their ballots, but also to the way information on ballots is combined to determine a winner. The most important properties of electoral systems, those that determine how well the winner reflects the voters’ preferences, can be formulated mathematically. So far, no electoral system free from undesirable properties has been identified, suggesting that the choice of an electoral system amounts to a trade-off of properties. This session explores the difficulty of finding and implementing a “good” electoral system. Even such simple desiderata as “one-voter, one-vote” have proven extremely difficult to achieve in practice. Mathematical study of such fairness-related properties typically finds systems that are successful on some dimensions but unsuccessful on others. Simulation or empirical study can be used to assess the frequency with which properties fail under particular electoral systems.