Preference Aggregation Method Research Articles

A preference aggregation method through the estimation of utility intervals

In this paper, a preference aggregation method is developed for ranking alternative courses of actions by combining preference rankings of alternatives given on individual criteria or by individual decision makers. In the method, preference rankings are viewed as constraints on alternative utilities, which are normalized, and linear programming models are constructed to estimate utility intervals, which are weighted and averaged to generate an aggregated utility interval. A simple yet pragmatic interval ranking method is used to compare and/or rank alternatives. The final ranking is generated as the most likely ranking with certain degrees of belief. Three numerical examples are examined to illustrate the potential applications of the proposed method. Scope and purpose The aggregation of preference rankings has wide applications in group decision making, social choice, committee election and voting systems. The purpose of this paper is to develop a preference aggregation method through the estimation of utility intervals, in which preference rankings are associated with utility intervals that are estimated using linear programming models and aggregated using the simple additive weighting method.

On consistency of the weighted geometric mean complex judgement matrix in AHP

The weighted geometric mean method (WGMM) is the most common group preference aggregation method in the Analytic Hierarchy Process. This paper reports on research concerning the consistency of WGMM and proves that the weighted geometric mean complex judgement matrix (WGMCJM) is of acceptable consistency. In Saaty's (T.L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, 1980) opinion, a consistency ratio (CR) of 0.1 or less is acceptable under the condition that all judgement matrices given by experts for the same problem of decision-making are of acceptable consistency. Accordingly, a theoretic basis has been developed for the application of the WGMM in group decision making.

On the difficulty of making social choices

The difficulty of making social choices seems to take on two forms: one that is related to both preferences and the method used in aggregating them and one which is related to the preferences only. In the former type the difficulty has to do with the discrepancies of outcomes resulting from various preference aggregation methods and the computation of winners in elections. Some approaches and results which take their motivation from the computability theory are discussed. The latter ‘institution-free’ type of difficulty pertains to solution theory of the voting games. We discuss the relationships between various solution concepts, e.g. uncovered set, Banks set, Copeland winners. Finally rough sets are utilized in an effort to measure the difficulty of making social choices.

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.