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Mathematical Support for the Geometric Mean when Deriving a Consistent Matrix from a Pairwise Ratio Matrix

Choo E. U., Wedley W. C., Wijnmalen D. J. D.

Fundamenta Informaticae

2016

Vol. 144, nr 3/4

263--278

A ratio pairwise comparison matrix estimates another matrix of true ratios between objects. From the pairwise comparison matrix, various methods are used to derive a priority vector and associated consistent matrix that also estimates the matrix of true ratios. The distance from the consistent matrix and the true matrix measures the accuracy of a method. The geometric mean is shown to be the only method with error below a basic threshold while being invariant to any reordering and rescaling of columns. Besides being simple to calculate, the geometric mean has excellent performance and many desirable properties.