Technical Note—The Effectiveness of Ordinal Dominance in Decision Analysis

Peter C. Fishburn and Irving H. LaValle
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Peter C. Fishburn: The Pennsylvania State University, University Park, Pennsylvania
Irving H. LaValle: Tulane University, New Orleans, Louisiana

Operations Research, 1974, vol. 22, issue 1, 177-180

Abstract: The easily applied technique of ordinal-dominance analysis in decisions under uncertainty eliminates inferior pure strategies. It is most applicable when the decision-maker’s consequence utilities are known only up to a monotonic transformation (ordinally). Each strategy eliminated by ordinal dominance will also be eliminated by cardinal dominance for every utility function that preserves the decision-maker’s preference order on the consequences. This note shows that, in finite decisions under uncertainty, if a pure strategy is not ordinally dominated, then there is some utility function that preserves the decision-maker’s preference order on the consequences such that the pure strategy is not cardinally dominated under this utility function. Hence ordinal-dominance analysis eliminates every pure strategy that can be safely eliminated when only the decision-maker's preference weak-ordering of the consequences is known.

Date: 1974
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