Non-Uniform Belief in Expected Utilities in Interval Decision Analysis

This paper demonstrates that second-order calculations add information about expected utilities when modeling imprecise information in decision models as intervals and employing the principle of maximizing the expected utility. Furthermore, due to the resulting warp in the distribution of belief over the intervals of expected utilities, the conservative Γmaximin decision rule seems to be unnecessarily conservative and pessimistic as the belief in neighborhoods of points near interval boundaries is significantly lower than in neighborhoods near the centre. Due to this, a generalized expected utility is proposed. Introduction In the basic model of Bayesian decision analysis, a decision maker is to choose an alternative/action from a nonempty, finite set A = {A1, . . . , An} of possible alternatives. Each alternative may end up with a finite set of consequences, and the resulting consequence of each alternative depends on the true (but probably unknown) state of nature θ ∈ Θ = {θ1, . . . , θi, . . . , θk}. The corresponding outcome is then evaluated by means of a utility function u satisfying u(A×Θ) → R (A, θ) → u(A, θ) Since the true state of nature is unknown, the model asserts the knowledge of the probability distribution P (.) on (Θ,Po(Θ)). The alternative A to choose is then the alternative which maximizes the expected utility, for all Ai ∈ A. This selection procedure is commonly referred to as the principle of maximizing the expected utility, and is argued for in (von Neumann and Morgenstern 1947) and (Savage 1972), as it is implied from widely accepted axiom systems defining formal models of rationality. Thus, a preference ordering relation on A is implied from the magnitudes of the different alternatives’ expected utility. Definition 1 The principle of maximizing the expected utility is accepted if a decision making agent chooses the alternative A∗, whenever A∗ = argmax A (E(A)) Copyright c © 2005, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. where E(A) = ∑