Technical Note—The Effectiveness of Ordinal Dominance in Decision Analysis

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.