An experiment on the numerical modelling of verbal ratio statements

Verbal statements are intuitively attractive for preference elicitation. In the analytic hierarchy process (AHP) the verbal responses to pairwise comparisons of relative importance are converted into real numbers according to the nine-point integer scale. Several alternative scales have been proposed for the conversion, but sufficient empirical evidence has not been produced to support the choice among these scales. The authors performed a comparative study in which subjects were requested to quantify verbal ratio statements by adjusting the heights of visually displayed bars. Subjects were also asked to employ verbal expressions in pairwise comparisons of areas of figures with different shapes. The principal result of the experiment was that the perceived meaning of the verbal expressions varies from one subject to the next and also depends on the set of elements involved in the comparisons. The results indicate that there are alternative numerical scales which yield more accurate estimates than the usual 1-to-9 scale and reduce the inconsistency of the comparison matrices. Alternative ways of using verbal preference statements are suggested to overcome the difficulties that arise from the context dependence of verbal pairwise comparisons.