The Tournament Tree Method for preference elicitation in Multi-criteria decision-making
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arXiv
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| Format: | Preprint |
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2025
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| author | García-Zamora, Diego Labella, Álvaro Figueira, José Rui |
| author_facet | García-Zamora, Diego Labella, Álvaro Figueira, José Rui |
| contents | Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high cognitive load required to complete $m(m-1)/2$ comparisons, the risk of inconsistency, and the computational complexity of deriving consistent value scales. This paper proposes the Tournament Tree Method (TTM), a novel elicitation and evaluation framework that overcomes these limitations. The TTM requires only $m-1$ pairwise comparisons to obtain a complete, reciprocal, and consistent comparison matrix. The method consists of three phases: (i) elicitation of expert judgments using a reduced set of targeted comparisons, (ii) construction of the consistent pairwise comparison matrix, and (iii) derivation of a global value scale from the resulting matrix. The proposed approach ensures consistency by design, minimizes cognitive effort, and reduces the dimensionality of preference modeling from $m(m-1)/2$ to $m$ parameters. Furthermore, it is compatible with the classical Deck of Cards method, and thus it can handle interval and ratio scales. We have also developed a web-based tool that demonstrates its practical applicability in real decision-making scenarios. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08197 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Tournament Tree Method for preference elicitation in Multi-criteria decision-making García-Zamora, Diego Labella, Álvaro Figueira, José Rui Artificial Intelligence Information Theory Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high cognitive load required to complete $m(m-1)/2$ comparisons, the risk of inconsistency, and the computational complexity of deriving consistent value scales. This paper proposes the Tournament Tree Method (TTM), a novel elicitation and evaluation framework that overcomes these limitations. The TTM requires only $m-1$ pairwise comparisons to obtain a complete, reciprocal, and consistent comparison matrix. The method consists of three phases: (i) elicitation of expert judgments using a reduced set of targeted comparisons, (ii) construction of the consistent pairwise comparison matrix, and (iii) derivation of a global value scale from the resulting matrix. The proposed approach ensures consistency by design, minimizes cognitive effort, and reduces the dimensionality of preference modeling from $m(m-1)/2$ to $m$ parameters. Furthermore, it is compatible with the classical Deck of Cards method, and thus it can handle interval and ratio scales. We have also developed a web-based tool that demonstrates its practical applicability in real decision-making scenarios. |
| title | The Tournament Tree Method for preference elicitation in Multi-criteria decision-making |
| topic | Artificial Intelligence Information Theory |
| url | https://arxiv.org/abs/2510.08197 |