An exaluation of judgment scale in the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) of Thomas L. Saaty is a popular method for decision making. In the AHP, data on decision maker's (DM's) pair-wise comparison are aggregated, and the degree of importance of each alternative is quantified. This results in not only the identification of the most important alternative but also the ranking of all alternatives for each DM. Various judgment scales have been proposed and put to use in the process of pair-wise comparison. Saaty advocated a 1–9 linear scale and claimed that this scale is consistent with the laws of physics. This linear scale invited some criticisms in the literature. The objections mainly stem from rank reversal and inconsistency. The objective of this paper is to find a scale appropriate for representing DM's perception. Specifically, we compare two scales: linear and power scales. The criteria of appropriateness are robustness with respect to scale change and consistency. Two types of data are used in the paper: (1) randomly generated data, and (2) data on political consciousness (survey carried out over Mie prefecture in February 1997). The results offer some evidence that power scale is preferable to linear scale as the judgment scale.