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 powerfu l techniques for decision making. A detailed survey of the literature has revealed that there exists no formal evaluation of the group prefe rence aggregation methods currently employed in AHP. This paper provid es such an evalaution using well established social choice axioms, whi ch govern the process of combining individual opinions to obtain a sin gle group opinion. The Geometric Mean Method (GMM) and the Weighted Ar ithmetic Mean Method (WAMM) are the two methods evaluated. It is shown , using counter-examples, that the GMM does not always satisfy the Par eto optimality axiom, which is one of the prominent and widely accepte d social choice axioms. This finding is significant as the GMM has bee n the most commonly used method in AHP for combining individual opinio ns to form a group opinion. The other method, viz. WAMM has satisfied all the axioms, except the 'independence of irrelevant alternatives' a xiom. In order to use the WAMM, one has to find the weightages (import ance) to be assigned to the members of the group. This is often a diff icult task, especially so if the group is large as in the case of publ ic policy decisions and when judgements are elicited through the use o f questionnaires. These situations need an objective method to derive members' weightages but only a few studies are available in the litera ture to address such a situation. We propose a simple and intuitively appealing eigenvector based method to intrinsically determine the weig htages for group members using their own subjective opinions. The supe riority of the proposed method over the previous methods is brought ou t in the paper.