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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
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    References listed on IDEAS

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