An alternative scaling method for priorities in hierarchical structures

The early contributions of Saaty have spawned a multitude of applications of principal right (PR) eigenvector “scaling” of a dominance matrix [R]. Prior to Saaty's work (1977–1984) scaling of dominance matrices received little attention in multidimensional scaling, e.g., see Shepard (1972, pp. 26–27). This eigenvector method (EM) of scaling [R] yields u_i scores (weights) popularly used at each branching of the Analytic Hierarchy Process (AHP) technique that has been increasingly applied in multiple criterion analysis of utility, preference, probability, and performance. In this paper, it is proposed that an alternate least squares method (LSM) scaling technique yielding least squares optimal scores (weights) provides $\text{w}{}_{\mathrm{i}}{}^1$ values having a number of important advantages over u_i scores popularly utilized to date.