Use of Second Order Stochastic Dominance in Decision Aiding.
Abstract
In this paper, we examine a single-stage, multiobjective decisionmaking problem under uncertainty. The decisionmaker can select any one of a finite number of alternatives. After any alternative is chosen, one of a finite number of outcomes will result. The probabilistics relationship between each alternative and each outcome is presumed to be known. We assume that all that is known about the decisionmaker is that he or she is risk adverse. Our objective is to determine the smallest subset of alternatives that is guaranteed to contain the most preferred alternative on the basis of this assumption. The achievement of this objective presumably enhances decisionmaking since alternative selection is generally easier if made from a subset of the alternative set rather than from the entire alternative set. The intent of this paper is to present an approach which achieves this objective and which has computational times amenable to interactive decision aiding. We make use of a fact, due to Fishburn and Vickson, which states that the feasibility of a certain collection of linear equalities and inequalities represents a necessary and sufficient condition for one alternative to be weakly preferred to another with respect to the second order stochastic dominance (SSD) relation. The approach presented here uses transitivity and upper and lower bounds on this relation in order to reduce the number of concomitant linear programs necessary for solution. The lower bound is provided by the first order stochastic dominance relation; the upper bound is given by a relation that is equivalent to the second order stochastic dominance relation when certain independence conditions hold. An example illustrates these results. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1981
- Accession Number
- ADA097117
Entities
People
- Andrew P. Sage
- Chelsea C. White
Organizations
- University of Virginia