Definition
Expected Utility Theory (EUT) is a framework for making rational decisions under uncertainty. It states that an agent should choose the action that maximizes the weighted average of all possible outcomes, where the weight of each outcome is its probability multiplied by its subjective value (utility). Formally:
- How to read: “The expected utility equals the sum from i equals one to n of P i times U of i.”
- Meaning: Weight each outcome’s subjective value by its probability—rational choice maximizes this sum under uncertainty.
Why It Matters
In a non-deterministic universe, “certainty” is a mirage, and EUT provides the mathematical tool for navigating a world of gray shades. It explains why rational agents buy insurance and how they should evaluate high-stakes bets, ensuring that decisions maximize long-term fulfillment rather than just short-term survival.
Core Concepts
- Subjective Utility: Unlike raw money or resources, utility accounts for the “diminishing marginal returns” of value (e.g., the first $1 million is worth more than the tenth).
- Risk Aversion: EUT explains why rational actors buy insurance; they prefer a smaller, certain loss to a tiny probability of a catastrophic loss.
- Bayesian Framework: Rational agents update their probability distributions () based on new information before calculating expected utility (Bayesian Updating).
- The Von Neumann-Morgenstern Axioms: The four mathematical conditions (completeness, transitivity, continuity, independence) that a preference system must follow to be considered “rational” in the EUT sense.
- Allais Paradox: A famous challenge to EUT showing that human choices often violate the theory’s axioms, revealing innate biases in how we perceive probability.