A Single-Stage Approach to Anscombe and Aumann's Expected Utility

Anscombe and Aumann showed that if one accepts the existence of a physical randomizing device such as a roulette wheel then Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their axioms. We demonstrate that the subjective expected utility derivation can be further simplified and need not invoke compound gambles. Our simplification is obtained by closely following the steps by which probabilities and utilities are elicited

A Single-Stage Approach to Anscombe and Aumann's Expected Utility

expected utility theory;decision analysis;revealed preference

Revealed likelihood and knightian uncertainty

expected utility theory;uncertainty;revealed preference

Sequential decision making with adaptive utility

Decision making with adaptive utility provides a generalisation to classical Bayesian decision theory, allowing the creation of a normative theory for decision selection when preferences are initially uncertain. The theory of adaptive utility was introduced by Cyert & DeGroot [27], but had since received little attention or development. In particular, foundational issues had not been explored and no consideration had been given to the generalisation of traditional utility concepts such as value of information or risk aversion. This thesis addresses such issues. An in-depth review of the decision theory literature is given, detailing differences in assumptions between various proposed normative theories and their possible generalisations. Motivation is provided for generalising expected utility theory to permit uncertain preferences, and it is argued that in such a situation, under the acceptance of traditional utility axioms, the decision maker should seek to select decisions so asto maximise expected adaptive utility . The possible applications of the theory forsequential decision making are illustrated by some small-scale examples, including examples of relevance within reliability theory

Theoretical and experimental investigation of explanations for the Ellsberg Paradox.

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