Using Principal Components Analysis for Aggregating Judgments in the Analytic Hierarchy Process

Often it is appropriate to have more than one decision maker perform the pairwise comparisons that are part of the Analytic Hierarchy Process (AHP). With group judgments one would hope for broad consensus among the decision makers, in which case one would aggregate judgments via their geometric mean. However, consensus may not always be reached and significant dispersion may exist among the judgments. The question arises as to what would be an appropriate aggregation scheme in such situations. Too much dispersion violates the principle of Pareto Optimality at the comparison and/or matrix levels, so that the group may be homogenous in some comparisons and heterogeneous in others. We propose a new aggregation method when the raw geometric mean cannot be used and the decision makers’ judgments cannot be revised. Our method makes use of principal components analysis (PCA) to combine the judgments into one aggregated value for each pairwise comparison. We show that this approach is equivalent to using a weighted geometric mean with the weights obtained from the PCA. ISAHP Article: Scala, Rajgopal, Vargas, Needy/Group Decision Making with Dispersion in the Analytic Hierarchy Process To Be Submitted to the International Symposium of the Analytic Hierarchy Process 2014, Washington D.C., U.S.A. International Symposium of the Analytic Hierarchy Process 2 Washington, D. C. June 29 – July 2, 2014