Eigenvector Method and Rank Reversal in Group Decision Making Revisited

• Autorzy: Csató L.

Identyfikatory

DOI

10.3233/FI-2017-1602

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

preference aggregation; pairwise comparison matrix; axiomatic approach; rank reversal; eigenvector method

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 156, nr 2
• Strony: 169--178
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Csató L.

• 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

Bibliografia

• [1] Pérez J, Mokotoff E. Eigenvector Priority Function Causes Strong Rank Reversal in Group Decision Making. Fundamenta Informaticae, 2016;144(3-4):255–261. URL http://dx.doi.org/10.3233/FI-2016-1333.
• [2] Saaty TL, Vargas LG. The legitimacy of rank reversal. Omega, 1984;12(5):513–516. URL https://doi.org/10.1016/0305-0483(84)90052-5.
• [3] Barzilai J, Golany B. AHP rank reversal, normalization and aggregation rules. INFOR: Information Systems and Operational Research, 1994;32(2):57–64. URL http://dx.doi.org/10.1080/03155986.1994.11732238.
• [4] Schenkerman S. Avoiding rank reversal in AHP decision-support models. European Journal of Operational Research, 1994;74(3):407–419. URL https://doi.org/10.1016/0377-2217(94)90220-8.
• [5] Wang YM, Elhag TMS. An approach to avoiding rank reversal in AHP. Decision Support Systems, 2006;42(3):1474–1480. URL https://doi.org/10.1016/j.dss.2005.12.002.
• [6] Wang YM, Luo Y. On rank reversal in decision analysis. Mathematical and Computer Modelling, 2009;49(5-6):1221–1229. URL https://doi.org/10.1016/j.mcm.2008.06.019.
• [7] Maleki H, Zahir S. A comprehensive literature review of the rank reversal phenomenon in the Analytic Hierarchy Process. Journal of Multi-Criteria Decision Analysis, 2013;20(3-4):141–155. URL http://dx.doi.org/10.1002/mcda.1479.
• [8] Hou F. A Hierarchical Decision Model Based on Pairwise Comparisons. Fundamenta Informaticae, 2016;144(3-4):333–348. URL http://dx.doi.org/10.3233/FI-2016-1339.
• [9] Koczkodaj WW, Mikhailov L, Redlarski G, Soltys M, Szybowski J, Tamazian G, Wajch E, Yuen KKF. Important facts and observations about pairwise comparisons. Fundamenta Informaticae, 2016;144(3-4):291–307. URL http://dx.doi.org/10.3233/FI-2016-1336.
• [10] Saaty TL. The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill, New York, 1980. ISBN:0070543712, 9780070543713.
• [11] Fichtner J. Some thoughts about the mathematics of the Analytic Hierarchy Process. Technical report, Institut für Angewandte Systemforschung und Operations Research, Universität der Bundeswehr München, 1984.
• [12] Fichtner J. On deriving priority vectors from matrices of pairwise comparisons. Socio-Economic Planning Sciences, 1986;20(6):341–345. URL http://www.sciencedirect.com/science/article/pii/0038-0121(86)90045-5.
• [13] Barzilai J, Cook WD, Golany B. Consistent weights for judgements matrices of the relative importance of alternatives. Operations Research Letters, 1987;6(3):131–134. URL http://dx.doi.org/10.1016/0167-6377(87)90026-5.
• [14] Cook WD, Kress M. Deriving weights from pairwise comparison ratio matrices: An axiomatic approach. European Journal of Operational Research, 1988;37(3):355–362. URL http://dx.doi.org/10.1016/0377-2217(88)90198-1.
• [15] Bryson N. A goal programming method for generating priority vectors. Journal of the Operational Research Society, 1995;46(5):641–648. URL https://doi.org/10.1057/jors.1995.88.
• [16] Barzilai J. Deriving weights from pairwise comparison matrices. Journal of the Operational Research Society, 1997;48(12):1226–1232. URL http://dx.doi.org/10.2307/3010752.
• [17] Dijkstra TK. On the extraction of weights from pairwise comparison matrices. Central European Journal of Operations Research, 2013;21(1):103–123. URL http://dx.doi.org/10.1007/s10100-011-0212-9.
• [18] Csató L. A characterization of the Logarithmic Least Squares Method, 2017. Manuscript.
• [19] Csató L, Rónyai L. Incomplete pairwise comparison matrices and weighting methods. Fundamenta Informaticae, 2016;144(3-4):309–320. URL http://dx.doi.org/10.3233/FI-2016-1337.
• [20] Chebotarev P, Shamis E. Characterizations of scoring methods for preference aggregation. Annals of Operations Research, 1998;80:299–332. URL http://dx.doi.org/10.1023/A:1018928301345.
• [21] González-Díaz J, Hendrickx R, Lohmann E. Paired comparisons analysis: an axiomatic approach to ranking methods. Social Choice and Welfare, 2014;42(1):139–169. URL http://hdl.handle.net/10.1007/s00355-013-0726-2.
• [22] Aczél J, Saaty TL. Procedures for synthesizing ratio judgements. Journal of Mathematical Psychology, 1983;27(1):93–102. URL https://doi.org/10.1016/0022-2496(83)90028-7.
• [23] Johnson CR, Beine WB, Wang TJ. Right-left asymmetry in an eigenvector ranking procedure. Journal of Mathematical Psychology, 1979;19(1):61–64. URL http://dx.doi.org/10.1016/0022-2496(79)90005-1.
• [24] Dodd FJ, Donegan HA, McMaster TBM. Inverse inconsistency in analytic hierarchies. European Journal of Operational Research, 1995;80(1):86–93. URL https://doi.org/10.1016/0377-2217(94)E0342-9.
• [25] Crawford G, Williams C. A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 1985;29(4):387–405. URL https://doi.org/10.1016/0022-2496(85)90002-1.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).