In three essays, my dissertation analyzes the dynamics of collegial decision making on three-judge panels of the U.S. Courts of Appeals, with a particular focus on how the judicial hierarchy interacts with collegiality to influence individual judicial voting. The first essay, “Panel Composition and Judicial Compliance on the U.S. Courts of Appeals,” presents a formal model that demonstrates how ideological polarization on a three-judge panel can affect the broader interactions between lower courts and the Supreme Court. The model shows that the presence of a single judge on a panel whose preferences are aligned with a higher court can induce compliance by the other two judges. The second essay, “Panel Composition and Voting on the U.S. Courts of Appeals Over Time,” examines the relationship between panel composition and judicial voting over time, showing that while the degree to which composition predicts votes has increased over the last 50 years, turnover in presidential party ensures that the majority of three-judge panels comprise at least one Democratic and Republican judge, thereby producing moderate judicial outcomes on the Courts of Appeals. The third essay, “Asymmetrical Incentives and Collegial Dynamics in the Judicial Hierarchy: Decision Making on Three-Judge Panels,” builds on the first two by investigating how the possibility of appellate review by both full circuits sitting together and the Supreme Court creates different incentives for individual judges on three-judge panels—incentives that lead to asymmetric voting patterns. I show that due to the presence of a conservative Supreme Court in recent decades, we should see larger ideological moderation among Democratic judges when sitting with a single Republican judge than vice versa, a prediction supported by empirical analysis of thousands of judicial votes. Taken together, the essays demonstrate the importance of placing collegial politics on three-judge panels within the broader context of the judicial hierarchy.