# Expected Utility Theory

## Definition

### Health Economics

- Expected utility theory postulates that a decision-maker chooses (sometimes, ought to choose) between risky or uncertain prospects by comparing their expected utility values. Essentially, the approach entails assuming that people maximize a weighted sum of utilities under uncertainty, where the weights are probabilities and choices are between gambles or lotteries containing goods and services of various kinds. The theory was developed in 18th-century Switzerland and became popular after it was formalized in the mid-20th century. There are many alternative formulations but each shares the key features of transitivity and continuity (common to all utility theories), completeness and von Neumann-Morgenstern (vNM) independence. Completeness implies that if lottery x is preferred to lottery y and lottery y is preferred to lottery z, then there is some combination of x and z that will be preferred to y. The vNM axiom means, roughly speaking, that adding a third lottery to two lotteries, whose ranking has already been determined, will not affect that ranking. This was also the beginning of game theory since expected utility theory's axioms were offered (and accepted by many influential scientists) as a justification for the use of expectations in game theory.

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