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The general problem addressed can be stated simply. A decision maker must choose among several alternatives A 1 , A 2 , …, A m , each of which will eventually result in a consequence describable in terms of a Single attribute X . The decision maker does not know exactly what consequence will result from each of the various alternatives, but he can assign probabilities to the various possibilities that might result from any course of action. What should he do? THE MOTIVATION FOR UTILITY THEORY The power of the concept of Utility and the grounds for our interest in it is as follows. If an appropriate Utility is assigned to each possible consequence and the expected Utility of each alternative is calculated, then the best course of action is the alternative with the highest expected Utility . Different sets of axioms that imply the existence of Utilities with the property that expected Utility is an appropriate guide for consistent decision making are presented in von Neumann and Morgenstern (1947), Savage (1954), Luce and Raiffa (1957), Pratt, Raiffa, and Schlaifer (1965), and Fishburn (1970). The next subsection informally reviews the basic ideas of the theory.
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