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Establishing dominance among alternatives under ambiguity
Abstract
When a decision analyst's goal is to establish a partial ordering of alternatives through dominance tests, then these dominance tests should incorporate ambiguities about outcomes and their likelihood in a manner consistent with the expressions of those providing information. Ambiguity is present, when, for example, one is provided with vague beliefs about how the future is expected to unfold, or imprecise specifications of the consequences of various actions. In general, ambiguity is a condition associated with the non-uniqueness of information caused by the existence of one-to-many, or more generally, many-to-many relations. This condition is prevalent in decision making, since we may have situations which associate one or many probabilities with one or many outcomes. This research addresses the following challenges: (1) Clarifying and representing beliefs about likelihood and outcomes as they are provided by sources. These representations of ambiguity utilize, but are not limited to, point representations, set representations (c.f. Dempster-Shafer theory), interval representations, and combinations of these. (2) Modifying and extending the stochastic dominance and mean-variance tests so that they may be useful when outcomes and probabilities are ambiguously described. This involves proposing and proving more general versions of the stochastic dominance theorems, developing foundational results in nonlinear programming, and developing accompanying models and procedures for determining mean-variance bounds. These extensions augment and complement sensitivity analysis, the traditional tool utilized for considering additional uncertainty in decision analysis. It can be shown that typical approaches to sensitivity analysis will not always yield the extreme values of the variance measures. The usefulness of the research is evident as one notes the widespread use of stochastic dominance and mean-risk tests and yet recognizes that decision-making under ambiguity is a prevalent condition. Decision makers who use such tests could pursue the task of ranking alternatives while explicitly recognizing existing ambiguities. Extending stochastic dominance theorems and mean-risk theorems provide valuable techniques to pare down the number of alternatives considered without burdening the decision maker to provide more information or express utilities or preferences for ambiguities.
Subject Area
Operations research|Statistics
Recommended Citation
Langewisch, Andrew T, "Establishing dominance among alternatives under ambiguity" (1998). ETD collection for University of Nebraska-Lincoln. AAI9903776.
https://digitalcommons.unl.edu/dissertations/AAI9903776