The Tournament Tree Method for preference elicitation in Multi-criteria decision-making

TL;DR

This work tackles the cognitive burden and inconsistency inherent in traditional pairwise preference elicitation for multi-criteria decision-making. It introduces the Tournament Tree Method (TTM), which uses only $m-1$ targeted questions in a tournament-like process to yield a complete, reciprocal, and consistent $m\times m$ preference matrix, from which a global value scale can be derived. The method formally links the elicited information to an additive score representation $M_{ij}=u_i-u_j$ and provides normalization and presentation that align with the Deck of Cards framework, enabling interval and ratio scales. A web-based tool demonstrates practical applicability, and the approach is argued to simplify computation relative to existing models while preserving the original judgments. Overall, TTM offers a scalable, explainable, and implementable alternative for preference elicitation in MCDM with potential for real-time decision support.

Abstract

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.

Figures (8)

• Figure 1: Step 1 of the TTM web-based tool.
• Figure 2: Step 2 of the TTM web-based tool.
• Figure 3: Step 3 (round 1) of the TTM web-based tool.
• Figure 4: Step 3 (round 2) of the TTM web-based tool.
• Figure 5: Step 4 of the TTM web-based tool.

Theorems & Definitions (20)

• Proposition 1
• proof
• Theorem 1
• proof
• Proposition 2
• proof
• Definition 1
• Example 1
• Definition 2
• Proposition 3