This course examines the foundational issues that arise in the study of mathematical models of decision-making at both the individual and group levels, and explores their key applications in philosophy, politics, and economics. The course is structured around three core areas: decision theory, which explores how individuals make choices under uncertainty; game theory, which analyzes strategic interactions among rational agents; and social choice theory, which investigates how groups arrive at collective decisions.

We will cover a range of topics, including ordinal and cardinal utility theory, the Allais and Ellsberg paradoxes, an introduction to game theory, voting methods and paradoxes, and utility aggregation. Core theorems such as May’s Theorem, Arrow’s Impossibility Theorem, and the Condorcet Jury Theorem will be critically examined. If time permits, we will also explore additional topics such as Newcomb's Paradox, strategic voting, Sen’s Impossibility of the Paretian Liberal, and the complexities of gerrymandering.

The readings for this course are interdisciplinary, drawing on sources from economics, philosophy, political science, psychology, and statistics.