A Graphical Analysis of Ratio-Scaled Paired Comparison Data

One of the building blocks of the Analytic Hierarchy Process (Saaty [Saaty, T. L. 1977. A scaling method for priorities in hierarchical structures. Math. Psych. 15 234--281.]) is the ratio-scaled assessment of an agent's preferences between pairs of alternatives. This article shows how it is possible to visualize such data and to detect cardinal and ordinal inconsistencies in the respondent's judgments. The graphical method used to display preferences is not new in itself: it dates back at least to the work of Gower (Gower, J. C. 1977. The analysis of asymmetry and orthogonality. J.-R. Barra, F. Brodeau, G. Romier, B. Van Cutsem, eds. Recent Developments in Statistics. North-Holland, Amsterdam, 109--123.), and many variants of his technique can be found in the literature. But Gower plots provide an especially valuable diagnostic tool in the context of AHP, as discussed and abundantly illustrated herein.