Analysis of Subjective Judgment Matrices.

A popular method for quantifying subjective judgment utilizes the dominant eigenvector of a matrix of paired comparisons. The eigenvector yields a scale of the importance of each element of a collection relative to the others. The scale is based on a matrix of subjective paired comparisons of elements of the collection. Thomas Saaty has shown this to be a useful tool for analyzing hierarchical structures in many military and industrial applications by estimating the scale at each level of a structured problem, this procedure yields the relative importance of the elements at the bottom level of the hierarchy to the goals or output at the top level. For this class of problems the geometric mean vector is computationally easier than statistically preferable to the eigenvector. Further, the geometric mean vector is applicable to a wider class of problems and has the advantage of arising from common statistical and mathematical models. The statistical advantages of the proposed procedure are theoretically and empirically demonstrated. Author