Glossary term
Expected Utility
Expected utility is the probability-weighted utility of possible outcomes, used to compare uncertain choices under risk.
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What Is Expected Utility?
Expected utility is the probability-weighted utility of possible outcomes. It is used to compare uncertain choices by asking not only what each outcome pays, but how much value or satisfaction the decision maker assigns to each outcome.
The concept is closely related to expected value, but it is not the same. Expected value weights dollar outcomes. Expected utility weights the utility of those outcomes. That distinction matters when risk, loss, wealth level, or personal preference changes how an outcome feels.
Key Takeaways
- Expected utility combines probabilities with the utility of possible outcomes.
- It can explain why people may prefer certainty over a higher expected dollar payoff.
- The concept is central to risk aversion, insurance, portfolio choice, and decision theory.
- Expected utility differs from expected value because it measures modeled value, not just dollars.
- Behavioral finance studies many situations where people depart from expected-utility predictions.
Expected Utility Formula
A simple expected utility calculation multiplies each outcome's utility by its probability and adds the results.
In this formula, EU is expected utility, pi is the probability of outcome i, and u(xi) is the utility assigned to outcome xi. The decision rule is to choose the option with the higher expected utility, assuming the model's conditions fit the decision.
Expected Utility Compared With Expected Value
Concept | What gets weighted | What it helps explain |
|---|---|---|
Expected value | Dollar or numerical payoff | Average payoff over repeated trials. |
Expected utility | Utility of each payoff | Risk preference and choice under uncertainty. |
Risk aversion | Declining marginal utility of wealth | Preference for certainty or insurance. |
Risk neutrality | Linear utility of money | Focus on expected payoff in pricing models. |
Where It Shows Up
Expected utility helps explain why someone might buy insurance even when the expected dollar payoff is less than the premium. Avoiding a severe loss may provide more utility than keeping the premium. It also helps explain why a retiree may prefer a smoother portfolio even if a riskier portfolio has a higher average expected return.
The concept appears in portfolio theory, game theory, economics, insurance, retirement planning, and derivatives pricing. It also gives behavioral finance a benchmark for identifying departures from traditional rational-choice models.
What the Model Does Not Capture
Expected utility assumes preferences can be represented in a stable and internally consistent way. Real decisions may depend on framing, recent losses, regret, ambiguity, social pressure, habits, or fear. A person may also react differently to gains and losses even when the dollar amounts are symmetrical.
That is why expected utility is best treated as a disciplined model rather than a complete portrait of human behavior. It clarifies how risk preferences can enter a decision, even when the real world adds messier layers.
The Bottom Line
Expected utility is a way to evaluate uncertain choices by weighting the utility of each possible outcome by its probability. It is useful because it explains risk preference in a way expected dollar value alone cannot.