Decision Theory Cheat Sheet
The core ideas of Decision Theory distilled into a single, scannable reference — perfect for review or quick lookup.
Quick Reference
Expected Utility Theory
A normative framework holding that a rational agent should choose the action that maximizes the weighted average of utilities across all possible outcomes, where weights are the probabilities of each outcome occurring.
Bayesian Decision Theory
An approach that combines Bayesian probability (updating beliefs based on evidence) with utility theory to determine optimal actions. The decision-maker assigns prior probabilities to uncertain states, updates them with new evidence, and chooses the action maximizing expected utility.
Decision Under Uncertainty vs. Risk
Decision under risk involves known probability distributions over outcomes, while decision under uncertainty (or ambiguity) involves unknown or imprecise probabilities. Different decision rules apply to each: expected utility works under risk, while maximin or minimax regret may apply under uncertainty.
Minimax and Maximin Strategies
Conservative decision rules for situations of deep uncertainty. Maximin selects the action whose worst-case outcome is best (maximizing the minimum payoff). Minimax regret selects the action that minimizes the maximum possible regret across all states of the world.
Von Neumann-Morgenstern Utility Theorem
A foundational result proving that if a decision-maker's preferences satisfy certain axioms (completeness, transitivity, continuity, and independence), then their preferences can be represented by a utility function, and they will act as if maximizing expected utility.
Rational Choice Theory
The framework assuming that individuals make decisions by selecting the option that best satisfies their preferences given their beliefs and constraints. It provides the theoretical backbone for much of economics, political science, and sociology.
Satisficing
A decision strategy introduced by Herbert Simon in which agents seek a solution that meets a minimum acceptability threshold rather than optimizing. This accounts for the cognitive costs of exhaustive search and computation.
The Ellsberg Paradox
A thought experiment demonstrating that people prefer known risks over unknown risks (ambiguity aversion), violating the independence axiom of expected utility theory. It reveals a systematic preference for betting on urns with known compositions over urns with unknown compositions.
Multi-Criteria Decision Analysis
A structured approach for evaluating alternatives against multiple, often conflicting objectives. Techniques include weighted scoring, the Analytic Hierarchy Process (AHP), and outranking methods that help decompose complex decisions into manageable comparisons.
Decision Trees
A graphical tool for mapping out sequential decisions and their possible outcomes, including chance events and payoffs at each branch. They help visualize the structure of a decision problem and calculate expected values through backward induction (folding back the tree).
Key Terms at a Glance
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