A Paired-Comparison Method for Interval Scaling

Abstract

A new method of analyzing paired-comparison data is presented: the linear paired-comparison (LPC) method. The LPC solves some deficiencies in the implementation of the eigenvector and geometric mean ratio hierarchy paired-comparison methods proposed by T. L. Saaty. In addition to formats typically used to collect paired-comparison data, an alternative format for collecting data is presented. Levels of significance with regard to rater consistency were evaluated for both the geometric mean and LPC methods, and it was found that levels of significance were not an adequate predictor of the proper ordinal ranking of the scale values for either method. A constant value for a consistency criterion is more appropriate. Saaty's criterion of an acceptable consistency index (CI) to judge a rater's consistency of CI ≤ 0.10 is defended. In addition, an appropriate value for the geometric mean method's rater consistency criterion, the residual mean square (S ²), was found to be S ² ≤ 0.27. For the LPC method, an acceptable criterion for the standard deviation from consistency (σ_c) was found to be σ_c ≤ 2.25.