Erwartungsnützlichkeit

Erwartungsnützlichkeit, a term originating from economics and decision theory, refers to the expected utility of a gamble or uncertain outcome. It is a fundamental concept for understanding how rational agents make choices when faced with risk. The calculation of Erwartungsnützlichkeit involves multiplying the utility of each possible outcome by its probability and then summing these products. Utility, in this context, represents the subjective value or satisfaction an individual derives from a particular outcome, which may not always be directly proportional to its monetary value.

For example, if an individual is presented with two options: receiving $100 with certainty or a 50% chance of receiving $250 and a 50% chance of receiving $0, they would calculate the Erwartungsnützlichkeit of the gamble. If the utility of $100 is U(100), and the utility of $250 is U(250), the Erwartungsnützlichkeit of the gamble would be 0.5 * U(250) + 0.5 * U(0). A rational agent, according to expected utility theory, will choose the option with the higher Erwartungsnützlichkeit.

The concept is crucial because it acknowledges that individuals do not solely base their decisions on expected monetary value. Risk aversion, for instance, is explained by the fact that the marginal utility of wealth typically decreases. This means that the pain of losing a certain amount of money is often perceived as greater than the pleasure of gaining the same amount, leading individuals to prefer a certain outcome over a gamble with an equivalent expected monetary value. Erwartungsnützlichkeit provides a framework to quantify these subjective preferences and predict decision-making under uncertainty.