## Decision Theory: Where Math and Philosophy Meet

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### Course Description

Suppose you are offered a game: you flip a fair coin. If the coin comes up heads, you win \$5. If the coin comes up tails, you lose \$1. Playing the game is free. Is it rational to play this game? To many, the obvious answer is “yes.” Though the chances of losing and winning are the same, you stand to win much more money than you stand to lose. Decision theory is a collection of mathematical, logical, and philosophical theories that systematizes and formalizes intuitions of this type, and has proved a powerful framework for thinking about the decision making of rational individuals.

Decision theory is the mostly widely used tool for calculating the rationality of choices, and it is at the heart of disciplines as varied as economics, statistics, business management, evolutionary biology, psychology, and political science. In this class, we will explore the details of this theory, starting by thinking about possible rules for making decisions under ignorance – such as dominance reasoning and the maximin rule. This will allow us to get clearer on concepts such as preference orderings and rational requirements. Next, we will prove the central theorem of decision theory: The Expected Utility Theorem. We will then examine the philosophical assumptions that the Expected Utility Theorem is built upon – assumptions that can (and perhaps should) be called into question. We will end by thinking about some of the philosophical puzzles that decision theory generates – puzzles such as the St. Petersburg Problem, Allais’s Paradox, the Two-Envelope Problem, and Newcomb’s Paradox.

Decision theory is an interdisciplinary field that is central to many disciplines.

By the end of this course, students will:
• learn the basics of the theory while gaining experience with formal systems – working with the concepts of proof and axioms
• learn important skills such as critical thinking, constructing and responding to arguments, and writing clearly about abstract topics

Students should have a good grasp of basic high-school level algebra.