Von Neumann-Morgenstern Utility Function

John von Neumann and Oskar Morgenstern extended the theory of consumer preferences by incorporating a theory of behavior toward risk variance. The utility function that bears their names arises from the expected utility hypothesis. Basically, when a consumer is faced with a choice of items or outcomes subject to various levels of chance, the optimal decision will be the one that maximizes the expected value of the utility (i.e., satisfaction) derived from the choice made. Expected value is the sum of the products of the various utilities and their associated probabilities. The consumer is expected to be able to rank the items or outcomes in terms of preference; but the expected value will be conditioned by their probability of occurrence.

The von Neumann-Morgenstern utility function can ...