AHP does not like compromises: the role of measurement scales

Analytic Hierarchy Process (AHP) is one of the most popular multi-attribute methods. However the results depend on the preference measurement scale used. In this paper we describe a decision problem with an inherent trade-off between two criteria. A decision maker has to choose among three alternatives: two extremes and one superior "compromise". Seven different measurement scales are considered for applying AHP. The results are compared with standard consumer choice theory. The power and the geometric scale are shown to be unsuitable because a compromise alternative will never be chosen regardless of the comparisons made by the consumer. Saaty's 1 to 9 scale and logarithm scale offer only few possibilities for the compromise to be selected and therefore should be avoided. The root square scale, the Ma and Zheng scale and the balanced scale offer a reasonable chance that a compromise alternative will be selected, and are hence more in agreement with consumer choice theory.