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UBC Theses and Dissertations

Studies in utility theory Larsson, Stig Owe

Abstract

Since vonNeumann and Morgenstern made their contributions, the expected utility criterion (EUC) has been the most accepted criterion in decision theory. Following their axiomatic approach justifying EUC, several other studies have been made suggesting the same criterion but under slightly different axiomatic systems. However, critics have found several simple decision problems (called paradoxes) which seem to contradict the conclusions of EUC; that is, the paradoxes contradict one or more of the axioms made to support EUC. The criticisms are based on empirical studies made in regard to the paradoxes. It is not always obvious, however, which axiom(s) is not accepted, since each approach to EUC gives a set of sufficient rather than necessary assumptions for EUC to hold. In Part I of the thesis a set of axioms which are necessary for EUC to hold is specified. Each of these axioms contains a basic assumption of a decision maker's behaviour. Therefore by considering the paradoxes in terms of these axioms, a better understanding is obtained with regard to which properties of EUC seem to be contradicted by the paradoxes. The conclusion of this study shows that most people contradict EUC because it does not differentiate between a "known" risk and an "unknown" risk. In Knight's terminology, there is a distinction between decision making under risk and uncertainty. Most empirical studies show that these differences are of such substantial proportions that there is a questionable justification for using the expected utility criterion for decision making under uncertainty. Although many alternatives to EUC for decision making under uncertainty exist, there are very few criteria for decision problems which fall between risk and uncertainty, that is, partial risk problems. Those existing are of an ad hoc nature. As a normative theory the EUC is far superior to any of these criteria in spite of its lack of distinction between risk and uncertainty. In the second part of the thesis an alternative normative criterion is suggested for decision making under partial risk and uncertainty. As an extension of EUC, this criterion distinguishes between risk and uncertainty. This theory expands on Ellsberg's suggestion that "ambiguity" influences one's preference among a set of alternatives. In this extension a more precise definition of "ambiguity" is needed and one is suggested here as a relation on the inner and outer measure of an event. The extension of EUC is then obtained by considering a more general set function, termed P-measure, which would depend on a set's ambiguity rather than a probability measure on the sets of rewards. It is concluded by an axiomatic development that the P-measure must be a non-negative mono-tonic set function which is not necessarily additive. It is also shown that the standard paradoxes related to paradoxes based on "known" versus "unknown" probabilities may be explained by this method and would therefore suggest an alternative to EUC for decision making under partial risk and uncertainty.

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