Ordinal judgments in multiattribute decision analysis

Abstract The article discusses the contradiction between the ambiguity of human judgment in a multicriterion environment and the exactness of the assessments required in the majority of the decision-making methods. Preferential information from the decision makers in the ordinal form (e.g., “more preferable”, “less preferable”, etc.) is argued to be more stable and more reliable than cardinal input. Ways of obtaining and using ordinal judgments for rank ordering of multiattribute alternatives are discussed. The effectiveness of the step-wise procedure of using ordinal tradeoffs for comparison of alternatives is evaluated. We introduce the notion of ordinal tradeoffs, presentation of ordinal tradeoffs as a flexible three-stage process, a paired joint ordinal scale (PJOS), and evaluation of the effectiveness of the three-stage process. Simulation results examine the sensitivity of the number of pairwise comparisons required for given numbers of criteria and categories within criteria, as well as the number of alternatives analyzed. This simulation shows that ordinal pairwise comparisons provide sufficient power to discriminate between 75% and 80% of the alternatives compared. While the proportional number of pairwise comparisons relative to the maximum possible decreases with the number of criteria and categories, the method is relatively insensitive to the number of alternatives considered.