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This paper presents the preference ratios in multiattribute evaluation (PRIME) method which supports the analysis of incomplete information in multiattribute weighting models. In PRIME, preference elicitation and synthesis is based on 1) the conversion of possibly imprecise ratio judgments into an imprecisely specified preference model, 2) the use of dominance structures and decision rules in deriving decision recommendations, and 3) the sequencing of the elicitation process into a series of elicitation tasks. This process may be continued until the most preferred alternative is identified or, alternatively, stopped with a decision recommendation if the decision maker is prepared to accept the possibility that the value of some other alternative is higher. An extensive simulation study on the computational properties of PRIME is presented. The method is illustrated with a re-analysis of an earlier case study on international oil tanker negotiations.

Five multiattribute weighting methods were compared in an Internet experiment. This is the first experiment where the subjects created the alternatives and attributes themselves. Each subject used five methods to assess attribute weights, one version of the Analytic Hierarchy Process (AHP), DIRECT weighting, Simple Multiattribute Rating Technique (SMART), SWING weighting and TRADEOFF weighting. They can all be used following the principles of multiattribute value theory. Furthermore, each of them asks decision makers to give numerical estimates of weight ratios although the elicitation questions are different. In earlier studies, however, these methods have yielded different weights. Our results suggest that weights are different because the methods explicitly or implicitly lead the decision makers to choose their responses from a limited set of numbers. The other consequences are that the spread of weights and the inconsistency between the preference statements depend on the number of attributes that a decision maker considers simultaneously.

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In this paper we apply multiattribute value theory as a framework for examining the use of pairwise comparisons in the analytic hierarchy process (AHP). On one hand our analysis indicates that pairwise comparisons should be understood in terms of preference differences between pairs of alternatives. On the other hand it points out undesirable effects caused by the upper bound and the discretization of any given ratio scale. Both these observations apply equally well to the SMART procedure which also uses estimates of weight ratios. Furthermore, we demonstrate that the AHP can be modified so as to produce results similar to those of multiattribute value measurement; we also propose new balanced scales to improve the sensitivity of the AHP ratio scales. Finally we show that the so-called supermatrix technique does not eliminate the rank reversal phenomenon which can be

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