A central problem for representative democracies is to design elections so that the representatives are an accurate reflection of the whole polity. A rigorous assessment of the effectiveness of an election design requires us to be able to measure things such as “representation” and “voting power” and to develop workable criteria for assessing when an election result is “accurate” and when it isn’t. Only then can we analyze whether a particular election design is likely to meet the criteria that have been developed. The goal of this course is to teach the various quantitative methods that have been developed—by courts and others—to address these questions, and consider how the courts have used or should use them in assessing issues in representation. The course will apply these methods to a broad range of election issues, including “one person-one vote,” equality of voting power, apportionment, gerrymandering, and polarized voting, among other concepts. We will also discuss what election methods are appropriate to address these varied problems. Although we will take a quantitative approach, there are no mathematical prerequisites.