Affiliations: [a] Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest (BCE) and MTA-BCE “Lendület” Strategic Interactions Research Group, Budapest, Hungary. [email protected] | [b] Informatics Laboratory, Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) and Budapest University of Technology and Economics (BME), Budapest, Hungary. [email protected]
Correspondence:
[†]
Address for correspondence: Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest (BCE), Hungary
Note: [*] We are grateful to Sándor Bozóki for reading the manuscript and for useful advice. The research was supported by OTKA grants K 111797, NK 105645, and by the Momentum Grant of the Hungarian Academy of Sciences.
Abstract: 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.
