A model for the relative importance of the criteria in the Multiplicative AHP and SMART

We define the relative importance of any pair of criteria as the substitution rate between the relative gains and losses of the alternatives when we move along an indifference curve. Under the geometric-mean aggregation rule in the Multiplicative AHP and under the arithmetic-mean aggregation rule in SMART, the relative (not the marginal) substitution rate depends neither on the performance of the alternatives under the remaining criteria nor on the units of performance measurement. Hence, it provides a sound argument for distributed decision-making processes where those who judge the criteria are not the same actors as those who assess the performance of the alternatives. The definition has a plausible basis in the psycho-physical research on the relationship between physical stimuli and sensory responses, which shows that human beings are sensitive, not to marginal but to relative changes of the stimulus intensities.