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An axiomatic model for MCDM using pairwise comparisons

Resource allocation problems are often subject to optimising with respect to multiple criteria which are difficult to quantify in conventional terms. Various techniques have been used to obtain objective functions which incorporate the idea of the relative value of competing options for resource. In this paper we build such a model. We show, up to accepting axioms on scales, scoring and aggregation, and using the method of pairwise comparisons, that there is only one model for scoring or valuing a set of options with respect to a hierarchy of criteria. The model allows for team decision making with respect to each criterion and we show that aggregation across teams is only possible under the strict use of appropriate scales. We show that there is a clear distinction to be made between the options using a category difference scale and the weighting of criteria using a ratio scale. The interaction between policy, as given by the hierarchy of weighted criteria, and the scores is clearly demonstrated.