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
    ---><---

    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.

    We have no bibliographic references for this item. You can help adding them by using 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.