Abstract
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.
Highlights
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
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
Stemming from philosophical concerns regarding the ability of decisionmaking 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]
Summary
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. Advances in Decision Sciences in this paper, combines multiattribute value trees with decision trees in a common model supporting intervalvalued weights, probabilities, and utilities together with a quantitative representation of qualitative statements such as “better than” and “more probable.” It handles overlapping expected utility intervals by means of an embedded form of sensitivity analysis; see Section 2 for a presentation. Second-order information can be used for expressing various beliefs over multidimensional spaces where each dimension corresponds to, for instance, possible probabilities or utilities of consequences These ideas have been collected in a conceptual model for decision analysis in [9] from which investigations on the implications of decision evaluation followed in, for example, [10, 11]. We emphasize how second-order information provides added value for decision evaluation in practice and provides an illustrative example together with some performance measures of the employed algorithms
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