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

Anna Tóth-Merényi, Csaba Mihálykó (), Éva Orbán-Mihálykó and László Gyarmati
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Anna Tóth-Merényi: Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary
Csaba Mihálykó: Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary
Éva Orbán-Mihálykó: Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary
László Gyarmati: Department of Mathematics, University of Pannonia, Egyetem u. 10., H-8200 Veszprém, Hungary

Mathematics, 2025, vol. 13, issue 9, 1-22

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.

Keywords: paired comparison; Davidson model; incomplete comparisons; consistency; optimal graph structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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