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Eigenvector Method and Rank Reversal in Group Decision Making Revisited

Csató L.

Fundamenta Informaticae

2017

Vol. 156, nr 2

169--178

It has been shown recently that the Eigenvector Method may lead to strong rank reversal in group decision making, that is, the alternative with the highest priority according to all individual vectors may lose its position when evaluations are derived from the aggregated group comparison matrix. We give a minimal counterexample and prove that this negative result is a consequence of the difference of the rankings induced by the right and inverse left eigenvectors.

Incomplete Pairwise Comparison Matrices and Weighting Methods

Csató L., Rónyai L.

Fundamenta Informaticae

2016

Vol. 144, nr 3/4

309--320

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the linear order preservation property if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.