Distribution of Expected Utility in Second-order Decision Analysis

In decision analysis maximising the expected utility is an often used approach in choosing the optimal alternative. But when probabilities and utilities are vague or imprecise expected utility is fraught with complications. Studying secondorder effects on decision analysis casts light on the importance of the structure of decision problems, pointing out some pitfalls in decision making and suggesting an easy to implement and easy to understand method of comparing decision alternatives. The topic of this thesis is such second-order effects of decision analysis, particularly with regards to expected utility and interval-bound probabilities. Explicit expressions for the second-order distributions inherent in interval-bound probabilities in general and likewise for distributions of expected utility for small decision problems are produced. By investigating these distributions the phenomenon of warping, that is concentration of belief, is studied.