%0 Journal Article
%T Implementing Second-Order Decision Analysis: Concepts, Algorithms, and Tool
%A Aron Larsson
%A Alina Kuznetsova
%A Ola Caster
%A Love Ekenberg
%J Advances in Decision Sciences
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/519512
%X We present implemented concepts and algorithms for a simulation approach to decision evaluation with second-order belief distributions in a common framework for interval decision analysis. The rationale behind this work is that decision analysis with interval-valued probabilities and utilities may lead to overlapping expected utility intervals yielding difficulties in discriminating between alternatives. By allowing for second-order belief distributions over interval-valued utility and probability statements these difficulties may not only be remedied but will also allow for decision evaluation concepts and techniques providing additional insight into a decision problem. The approach is based upon sets of linear constraints together with generation of random probability distributions and utility values from implicitly stated uniform second-order belief distributions over the polytopes given from the constraints. The result is an interactive method for decision evaluation with second-order belief distributions, complementing earlier methods for decision evaluation with interval-valued probabilities and utilities. The method has been implemented for trial use in a user oriented decision analysis software. 1. Introduction During the later decades decision analysis with imprecise or incomplete information has received a lot of attention within the area of utility theory based decision analysis. Stemming from philosophical concerns regarding the ability of decision-making agents to provide precise estimates of probabilities and utilities, as well as pragmatic concerns regarding the applicability of decision analysis, several approaches have been suggested, for example, approaches based on sets of probability measures [1] and interval probabilities [2]. With respect to methods for practical decision evaluation with imprecise input statements, a number of methods have been developed and some of them have been also implemented in computer software tools. Early works include the approach to decision making with linear partial information about input statements [3]. This approach promotes the conservative -maximin decision rule together with the use of imprecise probabilities modelled by means of linear constraints, suggesting evaluation algorithms to obtain minimum expected values. However, imprecision is restricted to probability assignments, and it is not possible to allow for constraints between different alternatives. Related methods aim at investigating whether stochastic dominance holds between decision alternatives when probabilities (and weights) are
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