Decision making modelisation in multi-criteria analysis using pairwise comparisons

We are concerned with the pairwise-comparison methods for solving the typical problem of multi-criteria decision analysis: the ranking and rating of a finite (usually small) number of alternatives under conflicting decison criteria. We are in fact running up against a two-level decision problem. At the first level, we estimate the weights of the decision criteria via a method of pairwise comparisons. At the second level, we estimate the weights of the alternatives in a similar way under each of the criteria separately. Lastly, we aggregate the results to obtain a final score for each alternative. In a method of pairwise comparisons, stimuli (criteria at decision level 1, and alternatives at level 2) are presented in pairs to one of more decision makers. The basic experiment is the comparison of two stimuli by a single decision maker who is requested to express his preference (if any) for one of the two. Our particular concern is the interface with the decision maker: the numerical scaling of the gradations of his comparative judgement. Well-known results in psychophysical measurement enable us to show that the echelons should exhibit a geometric progression.