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 second-order 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.

In explicatione consiliorum, maxima facere communis utilitas saepe trita ratio deligendi meliorem optionem est. Verum si probabilitates et utilitates incertae vel dubiae sint, communis utilitas perturbationes affert. Studium secundi ordinis effectuum in explicatione consiliorum explanat momentum structurae quaestionium consilii, insidias aliquas ad consilium capiendum indicat et facilem ad efficiendum et intellegendum rationem comparandi varia consilia suadet. Haec thesis tractat de secundi ordinis effectibus explicationis consilii, praesertim de commune utilitate et de probabilitatibus coniunctis intervallo. Voces apertae distributionum ordinis secundi in probabilitatibus intervallo conjunctis insitarum omnino et item distributionum utilitatis expectatae in parvis quaestionibus consiliorum eduntur. His distributionibus cognitis studetur res inflexionis, aliter dictu intentio fidei.