A General Theory of Subjective Probabilities and Expected Utilities

Publisher Summary This chapter discusses an expected utility theory. It presents a general theory for the usual subjective expected utility model for decision under uncertainty and a concise proof of a general expected utility theorem. Given a set of reasonable assumptions concerning the decision maker's preferences over alternative horse lotteries, the chapter highlights the existence of a utility function and a subjective probability measure over the states of the world such that the decision maker acts as if the expected utility was maximized. The utility function is continuous and is uniquely defined up to a positive linear transformation. In few cases, the utility function is bounded. However, most utility functions are unbounded in at least one direction. For such utility functions, horse lotteries can be constructed that have arbitrarily large expected utility and an arbitrarily small probability of receiving a positive return.