IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v313y2024i2p708-717.html
   My bibliography  Save this article

Right-left asymmetry of the eigenvector method: A simulation study

Author

Listed:
  • Csató, László

Abstract

The eigenvalue method, suggested by the developer of the extensively used Analytic Hierarchy Process methodology, exhibits right-left asymmetry: the priorities derived from the right eigenvector do not necessarily coincide with the priorities derived from the reciprocal left eigenvector. This paper offers a comprehensive numerical experiment to compare the two eigenvector-based weighting procedures and their reasonable alternative of the row geometric mean with respect to four measures. The underlying pairwise comparison matrices are constructed randomly with different dimensions and levels of inconsistency. The disagreement between the two eigenvectors turns out to be not always a monotonic function of these important characteristics of the matrix. The ranking contradictions can affect alternatives with relatively distant priorities. The row geometric mean is found to be almost at the midpoint between the right and inverse left eigenvectors, making it a straightforward compromise between them.

Suggested Citation

  • Csató, László, 2024. "Right-left asymmetry of the eigenvector method: A simulation study," European Journal of Operational Research, Elsevier, vol. 313(2), pages 708-717.
    • Handle: RePEc:eee:ejores:v:313:y:2024:i:2:p:708-717
    DOI: 10.1016/j.ejor.2023.09.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221723007257
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2023.09.022?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fichtner, John, 1986. "On deriving priority vectors from matrices of pairwise comparisons," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 341-345.
    2. Vargas, Luis G., 1990. "An overview of the analytic hierarchy process and its applications," European Journal of Operational Research, Elsevier, vol. 48(1), pages 2-8, September.
    3. Szádoczki, Zsombor & Bozóki, Sándor & Tekile, Hailemariam Abebe, 2022. "Filling in pattern designs for incomplete pairwise comparison matrices: (Quasi-)regular graphs with minimal diameter," Omega, Elsevier, vol. 107(C).
    4. Ernest H. Forman & Saul I. Gass, 2001. "The Analytic Hierarchy Process---An Exposition," Operations Research, INFORMS, vol. 49(4), pages 469-486, August.
    5. Dodd, F. J. & Donegan, H. A. & McMaster, T. B. M., 1995. "Inverse inconsistency in analytic hierarchies," European Journal of Operational Research, Elsevier, vol. 80(1), pages 86-93, January.
    6. Tomashevskii, I.L., 2015. "Eigenvector ranking method as a measuring tool: Formulas for errors," European Journal of Operational Research, Elsevier, vol. 240(3), pages 774-780.
    7. Vaidya, Omkarprasad S. & Kumar, Sushil, 2006. "Analytic hierarchy process: An overview of applications," European Journal of Operational Research, Elsevier, vol. 169(1), pages 1-29, February.
    8. László Csató, 2018. "Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom," Group Decision and Negotiation, Springer, vol. 27(6), pages 1011-1027, December.
    9. R. Blanquero & E. Carrizosa & E. Conde, 2006. "Inferring Efficient Weights from Pairwise Comparison Matrices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 271-284, October.
    10. Zsombor Szádoczki & Sándor Bozóki & Patrik Juhász & Sergii V. Kadenko & Vitaliy Tsyganok, 2023. "Incomplete pairwise comparison matrices based on graphs with average degree approximately 3," Annals of Operations Research, Springer, vol. 326(2), pages 783-807, July.
    11. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 387-400, December.
    12. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    13. Csató, László & Petróczy, Dóra Gréta, 2021. "On the monotonicity of the eigenvector method," European Journal of Operational Research, Elsevier, vol. 292(1), pages 230-237.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bice Cavallo, 2019. "Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem," Journal of Global Optimization, Springer, vol. 75(1), pages 143-161, September.
    2. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Influence of aggregation and measurement scale on ranking a compromise alternative in AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 700-710, April.
    3. Csató, László & Petróczy, Dóra Gréta, 2021. "On the monotonicity of the eigenvector method," European Journal of Operational Research, Elsevier, vol. 292(1), pages 230-237.
    4. Fernandes, Rosário & Furtado, Susana, 2022. "Efficiency of the principal eigenvector of some triple perturbed consistent matrices," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1007-1015.
    5. Zsuzsanna Katalin Szabo & Zsombor Szádoczki & Sándor Bozóki & Gabriela C. Stănciulescu & Dalma Szabo, 2021. "An Analytic Hierarchy Process Approach for Prioritisation of Strategic Objectives of Sustainable Development," Sustainability, MDPI, vol. 13(4), pages 1-26, February.
    6. Ágoston, Kolos Csaba & Csató, László, 2024. "A lexicographically optimal completion for pairwise comparison matrices with missing entries," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1078-1086.
    7. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    8. Tekile, Hailemariam Abebe & Brunelli, Matteo & Fedrizzi, Michele, 2023. "A numerical comparative study of completion methods for pairwise comparison matrices," Operations Research Perspectives, Elsevier, vol. 10(C).
    9. Siraj, Sajid & Mikhailov, Ludmil & Keane, John A., 2015. "Contribution of individual judgments toward inconsistency in pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 242(2), pages 557-567.
    10. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Does AHP help us make a choice? An experimental evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1801-1812, October.
    11. D'ora Gr'eta Petr'oczy & L'aszl'o Csat'o, 2019. "Revenue allocation in Formula One: a pairwise comparison approach," Papers 1909.12931, arXiv.org, revised Dec 2020.
    12. Wenshuai Wu & Gang Kou, 2016. "A group consensus model for evaluating real estate investment alternatives," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-10, December.
    13. Lucas, Rochelle Irene & Promentilla, Michael Angelo & Ubando, Aristotle & Tan, Raymond Girard & Aviso, Kathleen & Yu, Krista Danielle, 2017. "An AHP-based evaluation method for teacher training workshop on information and communication technology," Evaluation and Program Planning, Elsevier, vol. 63(C), pages 93-100.
    14. Koray Altintas & Ozalp Vayvay & Sinan Apak & Emine Cobanoglu, 2020. "An Extended GRA Method Integrated with Fuzzy AHP to Construct a Multidimensional Index for Ranking Overall Energy Sustainability Performances," Sustainability, MDPI, vol. 12(4), pages 1-21, February.
    15. Xue Ding & Mengling Qin & Linsen Yin & Dayong Lv & Yao Bai, 2023. "Research on FinTech Talent Evaluation Index System and Recruitment Strategy: Evidence From Shanghai in China," SAGE Open, , vol. 13(4), pages 21582440231, November.
    16. Fatima Lambarraa-Lehnhardt & Rico Ihle & Hajar Elyoubi, 2021. "How Successful Is Origin Labeling in a Developing Country Context? Moroccan Consumers’ Preferences toward Local Products," Sustainability, MDPI, vol. 13(15), pages 1-17, July.
    17. Zhu, Bin & Xu, Zeshui, 2014. "Analytic hierarchy process-hesitant group decision making," European Journal of Operational Research, Elsevier, vol. 239(3), pages 794-801.
    18. Hocine, Amine & Kouaissah, Noureddine, 2020. "XOR analytic hierarchy process and its application in the renewable energy sector," Omega, Elsevier, vol. 97(C).
    19. Alessio Ishizaka & Enrique Mu, 2023. "What is so special about the analytic hierarchy and network process?," Annals of Operations Research, Springer, vol. 326(2), pages 625-634, July.
    20. James G. Dolan & Emily Boohaker & Jeroan Allison & Thomas F. Imperiale, 2013. "Patients’ Preferences and Priorities Regarding Colorectal Cancer Screening," Medical Decision Making, , vol. 33(1), pages 59-70, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:313:y:2024:i:2:p:708-717. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.