IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i9p1374-d1640387.html
   My bibliography  Save this article

Exploring Consistency in the Three-Option Davidson Model: Bridging Pairwise Comparison Matrices and Stochastic Methods

Author

Listed:
  • Anna Tóth-Merényi

    (Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary
    These authors contributed equally to this work.)

  • Csaba Mihálykó

    (Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary
    These authors contributed equally to this work.)

  • Éva Orbán-Mihálykó

    (Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary
    These authors contributed equally to this work.)

  • László Gyarmati

    (Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary
    These authors contributed equally to this work.)

Abstract

In this paper, data consistency in the three-option Davidson model is investigated. Starting out with the usual consistency definition in pairwise matrices-based methods, we examine its consequences. We formulate an equivalent statement based on the usual PCM-based consistency definition for evaluation results, which aligns with the statement found in the two-option model and establishes a connection between the evaluation results based on PCM and those obtained from the three-option Davidson model. The theoretical results are complemented by findings based on random simulations, through which we also demonstrate the connections: the optimal comparison structures are identical to those in the PCM-based methods and in the two-option Bradley–Terry model.

Suggested Citation

  • Anna Tóth-Merényi & Csaba Mihálykó & Éva Orbán-Mihálykó & László Gyarmati, 2025. "Exploring Consistency in the Three-Option Davidson Model: Bridging Pairwise Comparison Matrices and Stochastic Methods," Mathematics, MDPI, vol. 13(9), pages 1-22, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1374-:d:1640387
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/9/1374/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/9/1374/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Saaty, Thomas L., 2003. "Decision-making with the AHP: Why is the principal eigenvector necessary," European Journal of Operational Research, Elsevier, vol. 145(1), pages 85-91, February.
    2. Ágoston, Kolos Csaba & Csató, László, 2022. "Inconsistency thresholds for incomplete pairwise comparison matrices," Omega, Elsevier, vol. 108(C).
    3. Baker, Rose D. & McHale, Ian G., 2014. "A dynamic paired comparisons model: Who is the greatest tennis player?," European Journal of Operational Research, Elsevier, vol. 236(2), pages 677-684.
    4. 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.
    5. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    6. Saaty, Thomas L., 1990. "How to make a decision: The analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 48(1), pages 9-26, September.
    7. Piet Verschuren & Bas Arts, 2005. "Quantifying influence in complex decision making by means of paired comparisons," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(5), pages 495-516, January.
    8. Bozóki, Sándor & Csató, László & Temesi, József, 2016. "An application of incomplete pairwise comparison matrices for ranking top tennis players," European Journal of Operational Research, Elsevier, vol. 248(1), pages 211-218.
    9. Alan Agresti, 1992. "Analysis of Ordinal Paired Comparison Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 287-297, June.
    10. Mangla, Sachin Kumar & Kumar, Pradeep & Barua, Mukesh Kumar, 2015. "Risk analysis in green supply chain using fuzzy AHP approach: A case study," Resources, Conservation & Recycling, Elsevier, vol. 104(PB), pages 375-390.
    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. Madjid Tavana & Mariya Sodenkamp & Leena Suhl, 2010. "A soft multi-criteria decision analysis model with application to the European Union enlargement," Annals of Operations Research, Springer, vol. 181(1), pages 393-421, December.
    2. Éva Orbán-Mihálykó & Csaba Mihálykó & László Koltay, 2019. "A generalization of the Thurstone method for multiple choice and incomplete paired comparisons," 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. 27(1), pages 133-159, March.
    3. 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.
    4. Zhu, Bin & Xu, Zeshui & Zhang, Ren & Hong, Mei, 2016. "Hesitant analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 250(2), pages 602-614.
    5. AlSabbagh, Maha & Siu, Yim Ling & Guehnemann, Astrid & Barrett, John, 2017. "Integrated approach to the assessment of CO2e-mitigation measures for the road passenger transport sector in Bahrain," Renewable and Sustainable Energy Reviews, Elsevier, vol. 71(C), pages 203-215.
    6. Vivek Agrawal & Rajendra P. Mohanty & Sucheta Agarwal & Jitendra Kumar Dixit & Anand M. Agrawal, 2023. "Analyzing critical success factors for sustainable green supply chain management," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(8), pages 8233-8258, August.
    7. R. Jothi Basu & Nachiappan Subramanian & Angappa Gunasekaran & P. L. K. Palaniappan, 2017. "Influence of non-price and environmental sustainability factors on truckload procurement process," Annals of Operations Research, Springer, vol. 250(2), pages 363-388, March.
    8. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Dai, Min, 2008. "A comparative study of the numerical scales and the prioritization methods in AHP," European Journal of Operational Research, Elsevier, vol. 186(1), pages 229-242, April.
    9. Kang Xu & Jiuping Xu, 2020. "A direct consistency test and improvement method for the analytic hierarchy process," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 359-388, September.
    10. Ting Kuo & Ming-Hui Chen, 2022. "On Indeterminacy of Interval Multiplicative Pairwise Comparison Matrix," Mathematics, MDPI, vol. 10(4), pages 1-18, February.
    11. Ergu, Daji & Kou, Gang & Peng, Yi & Shi, Yong, 2011. "A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP," European Journal of Operational Research, Elsevier, vol. 213(1), pages 246-259, August.
    12. S Taghipour & D Banjevic & A K S Jardine, 2011. "Prioritization of medical equipment for maintenance decisions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1666-1687, September.
    13. Mehmet Yüksel, 2019. "A Model Proposal for the Evaluation of Chemistry Education in the Context of Learning Environment," Asian Journal of Education and Training, Asian Online Journal Publishing Group, vol. 5(3), pages 488-494.
    14. Liu, Min & Heijman, Wim & Zhu, Xueqin & Dries, Liesbeth & Huang, Jikun, 2015. "Individual and Social Optima of Rural Land Allocation by Stakeholders: A Case Study on Eco-fragile Areas of Nothern China," 2015 Conference, August 9-14, 2015, Milan, Italy 212051, International Association of Agricultural Economists.
    15. Bernasconi, Michele & Choirat, Christine & Seri, Raffaello, 2014. "Empirical properties of group preference aggregation methods employed in AHP: Theory and evidence," European Journal of Operational Research, Elsevier, vol. 232(3), pages 584-592.
    16. Vicente Rodríguez Montequín & Joaquín Manuel Villanueva Balsera & Marina Díaz Piloñeta & César Álvarez Pérez, 2020. "A Bradley-Terry Model-Based Approach to Prioritize the Balance Scorecard Driving Factors: The Case Study of a Financial Software Factory," Mathematics, MDPI, vol. 8(2), pages 1-15, February.
    17. L. N. Pradeep Kumar Rallabandi & Ravindranath Vandrangi & Subba Rao Rachakonda, 2016. "Improved Consistency Ratio for Pairwise Comparison Matrix in Analytic Hierarchy Processes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-19, June.
    18. Karanik, Marcelo & Wanderer, Leonardo & Gomez-Ruiz, Jose Antonio & Pelaez, Jose Ignacio, 2016. "Reconstruction methods for AHP pairwise matrices: How reliable are they?," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 103-124.
    19. Antonella Basso & Stefania Funari, 2020. "A three-system approach that integrates DEA, BSC, and AHP for museum evaluation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 413-441, December.
    20. Mendes, Paulo & Leal, José Eugênio & Thomé, Antônio Márcio Tavares, 2016. "A maturity model for demand-driven supply chains in the consumer product goods industry," International Journal of Production Economics, Elsevier, vol. 179(C), pages 153-165.

    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:gam:jmathe:v:13:y:2025:i:9:p:1374-:d:1640387. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.