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.

翻译：成对比较数据在体育、社会选择与机器学习等领域被广泛用于推断潜在排序。布拉德利-特里模型提供了基础的概率框架，但其本质上假设偏好具有传递性，仅通过主体特定参数解释所有比较结果。然而在许多竞争性网络中，环路诱导效应是内在固有的，忽略此类效应将导致估计与不确定性量化的失真。为克服这一局限，我们提出一种显式分离传递性与非传递性分量的布拉德利-特里模型贝叶斯扩展。所提出的贝叶斯非传递性布拉德利-特里模型将组合霍奇理论嵌入逻辑斯蒂框架，将成对关系分解为表征传递性强度的梯度流与捕捉环路诱导结构的旋度流。我们对旋度分量施加全局-局部收缩先验，实现数据自适应正则化，并确保在无非传递性时自然退化为经典布拉德利-特里模型。后验推断采用高效吉布斯采样器实现，提供可扩展计算与完整的贝叶斯不确定性量化。仿真研究表明，相较于现有处理非传递性的贝叶斯模型，本方法在估计精度、不确定性校准及计算效率方面均有显著提升。该框架能够在全局与三元组层面实现不确定性感知的非传递性量化，同时刻画团队间由竞争环路诱导的竞争优势。