Affiliations: Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision Systems, Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Kende street 13-17, 1111 Budapest, Hungary. [email protected]
Correspondence:
[†]
Address for correspondence: Laboratory on Engineering and Management Intelligence, Research Group of Operations Research and Decision Systems, Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI), Kende street 13-17, 1111 Budapest, Hungary
Note: [*] I am grateful to Sándor Bozóki for useful advices. Three anonymous reviewers provided valuable comments and suggestions on earlier drafts. Also affiliated at: Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest (BCE), Fővám square 13-15, 1093 Budapest, Hungary.
Abstract: 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.
