Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios

Abstract

Three methods—the eigenvalue, logarithmic least squares, and least squares methods—used to derive estimates of ratio scales from a positive reciprocal matrix are analyzed. The criteria for comparison are the measurement of consistency, dual solutions, and rank preservation. It is shown that the eigenvalue procedure, which is metric-free, leads to a structural index for measuring inconsistency, has two separate dual interpretations and is the only method that guarantees rank preservation under inconsistency conditions.