Decomposition of variation in experts' judgments in the analytic hierarchy process

Although methods or techniques of aggregating preference or priority in the analytic hierarchy process (AHP) have been proposed to reconcile conflicts and differences among decision makers, the average-type manipulations usually ignore the variation or dispersion among experts, and are vulnerable to the extreme values (come from particular viewpoints or even represent some experts' effort in distorting the final ranking). In this study, we propose a regression approach for estimating the decision weights of AHP using linear mixed models (LMM). Other than determining the weight vectors, this model also allows us to decompose the variation or uncertainty in experts' judgment. In particular, the variation among experts and the residual uncertainty due to rounding errors in AHP scale or due to inconsistency within individual expert's judgments can be estimated and rigorously tested using well-known statistical theories. Other than characterizing different sources of uncertainty, this model allows us to rigorously test other factors that might significant affect weight assessments. Furthermore, several managerial implications on how the model results can be effectively used in decision making are identified.