Group Decision Making with Dispersion in the Analytic Hierarchy Process

Natalie M. Scala (), Jayant Rajgopal (), Luis G. Vargas () and Kim LaScola Needy ()
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Natalie M. Scala: Towson University
Jayant Rajgopal: University of Pittsburgh
Luis G. Vargas: University of Pittsburgh
Kim LaScola Needy: University of Arkansas

Group Decision and Negotiation, 2016, vol. 25, issue 2, No 6, 355-372

Abstract: Abstract With group judgments in the context of the Analytic Hierarchy Process (AHP) one would hope for broad consensus among the decision makers. However, in practice this will not always be the case, and significant dispersion may exist among the judgments. Too much dispersion violates the principle of Pareto Optimality at the comparison level and/or matrix level, and if this happens, then the group may be homogenous in some comparisons and heterogeneous in others. The question then arises as to what would be an appropriate aggregation scheme when a consensus cannot be reached and the decision makers are either unwilling or unable to revise their judgments. In particular, the traditional aggregation via the geometric mean has been shown to be inappropriate in such situations. In this paper, we propose a new method for aggregating judgments when the raw geometric mean cannot be used. Our work is motivated by a supply chain problem of managing spare parts in the nuclear power generation sector and can be applied whenever the AHP is used with judgments from multiple decision makers. The method makes use of principal components analysis (PCA) to combine the judgments into one aggregated value for each pairwise comparison. We show that this approach is equivalent to using a weighted geometric mean with the weights obtained from the PCA.

Keywords: Group decisions; Analytic Hierarchy Process; Geometric mean; Geometric dispersion; Principal component analysis; Weighted geometric mean (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10726-015-9445-7

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