The Bayesian Intransitive Bradley-Terry Model via Combinatorial Hodge Theory

Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive preferences, explaining all comparisons solely through subject-specific parameters. In many competitive networks, however, cycle-induced effects are intrinsic, and ignoring them can distort both estimation and uncertainty quantification. To address this limitation, we propose a Bayesian extension of the Bradley-Terry model that explicitly separates the transitive and intransitive components. The proposed Bayesian Intransitive Bradley-Terry model embeds combinatorial Hodge theory into a logistic framework, decomposing paired relationships into a gradient flow representing transitive strength and a curl flow capturing cycle-induced structure. We impose global-local shrinkage priors on the curl component, enabling data-adaptive regularization and ensuring a natural reduction to the classical Bradley-Terry model when intransitivity is absent. Posterior inference is performed using an efficient Gibbs sampler, providing scalable computation and full Bayesian uncertainty quantification. Simulation studies demonstrate improved estimation accuracy, well-calibrated uncertainty, and substantial computational advantages over existing Bayesian models for intransitivity. The proposed framework enables uncertainty-aware quantification of intransitivity at both the global and triad levels, while also characterizing cycle-induced competitive advantages among teams.

• Publication year

  2026

• Venue

  Unknown venue

• Publication date

  2026-01-12

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 2601.07158
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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