A simulation-based evaluation of the approximate and the exact eigenvector methods employed in the analytic hierarchy process

The Analytic Hierarchy Process (AHP) is a popular multi-criteria decision making method. It provides ratio-scale measurements of the priorities of elements in various levels of a hierarchy. These priorities are obtained through pairwise comparisons of elements in one level with reference to each element in the immediate higher level. Saaty has suggested two methods, viz., the approximate eigenvector method (AEV) and the exact eigenvector method (EEV) for calculating the priorities. Research on AHP has led to conflicting views on the use of these two methods. This paper presents a simulation analysis to evaluate them. The simulation analysis uses the concept of approximating a continuous pairwise comparison matrix by its closest discretized pairwise comparison matrix. This exercise supports Saaty's theoretical statements and empirically concludes that the EEV method is to be preferred over the AEV method for the calculation of priority vectors.