Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members' weightages

The Analytic Hierarchy Process (AHP) is one of the popular and powerful techniques for decision making. A detailed survey of the literature has revealed that there exists no formal evaluation of the group preference aggregation methods currently employed in AHP. This paper provides such an evaluation using well established social choice axioms, which govern the process of combining individual opinions to obtain a single group opinion. The Geometric Mean Method (GMM) and the Weighted Arithmetic Mean Method (WAMM) are the two methods evaluated. It is shown, using counter-examples, that the GMM does not always satisfy the Pareto optimality axiom, which is one of the prominent and widely accepted social choice axioms. This finding is significant as the GMM has been the most commonly used method in AHP for combining individual opinions to form a group opinion. The other method, viz. (WAMM) has satisfied all the axioms, except the ‘independence of irrelevant alternatives’ axiom. In order to use the WAMM, one has to find the weightages (importance) to be assigned to the members of the group. This is often a difficult task, especially so if the group is large as in the case of public policy decisions and when judgements are elicited through the use of questionnaires. These situations need an objective method to derive members' weightages but only a few studies are available in the literature to address such a situation. We propose a simple and intuitively appealing eigenvector based method to intrinsically determine the weightages for group members using their own subjective opinions. The superiority of the proposed method over the previous methods is brought out in the paper.