Bradley–Terry Model

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The Bradley–Terry model estimates how likely one item is to beat another from pairwise judgments, making it useful for ranking systems, people, and responses when direct scores are hard to assign. Common approaches include maximum-likelihood and spectral estimation, with extensions that model judge reliability, preference heterogeneity, ties, and nonlinear comparison links. Applications include sports and recommender rankings as well as language-model evaluation and preference-based reward learning. A central tension is that simple models assume comparisons reflect one stable underlying ordering, while real judgments can be inconsistent, context-dependent, or sensitive to which comparisons were collected.

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22 papers4 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Alternative Strategies for Active Learning with Bayesian Bradley Terry Model
Oct 21, 2026Saman Jayasinghe, Sean Walton, Alma Rahat +2Pairwise Ranking Active Preference Learning
Swansea University, United Kingdom · Loughborough University, United Kingdom · Bath Spa University, United Kingdom +1
Statistical Learning Theory for Direct Preference Optimization
Oct 19, 2026Joel Wills, Yuanfan Li, Yiming Ying +1Direct Preference Optimization Pairwise Preference Learning
School of Mathematics and Statistics, The University of Sydney
Similar Models, Broken Odds: Where Luce's Axiom Fails in Chatbot Arena
Oct 13, 2026Soovadeep Bakshi, Apurba Bose, Aishwarya Bose +1Discrete Choice Modeling Bradley–Terry Model
Independent Researcher.
How Many Repeated Pairwise Comparisons Are Needed for Ranking under Heterogeneity?
Oct 7, 2026Shashaank Aiyer, Han ShaoPairwise Ranking Pairwise Preference Learning
University of Maryland
Error Bounds for Statistical Estimators in BTL Model with Parametric Multivariate Utility Functions
Sep 22, 2026Yicheng Li, Huifu XuParameter Estimation Minimax Estimation
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong.
Multiple latent orderings better predict language model preferences
Aug 26, 2026Aviral Chawla, William H. W. Thompson, Jean-Gabriel YoungPreference Modeling Pairwise Preference Learning
Vermont Complex Systems Institute University of Vermont Burlington, Vermont 05403 · Vermont Complex Systems Institute Department of Statistics University of Vermont Burlington, Vermont 05403
Isotonic Bradley-Terry Model for Paired Comparison Data
Aug 3, 2026Ryoya YamasakiPairwise Preference Learning Pairwise Comparison
Hitotsubashi Institute for Advanced Study, Hitotsubashi University, 2-1 Naka, Kunitachi, 186-8601, Tokyo, Japan.
Convergence analysis of a family of Zermelo-type iterations for the Bradley--Terry model
Jul 24, 2026Ruijian Han, Ding Lu, Yiming XuOptimization Convergence Analysis Bradley–Terry Model
Department of Data Science and Artificial Intelligence, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR · Department of Mathematics, University of Kentucky, Lexington, KY, 40506, USA
On Generalizing Preference-based Reinforcement Learning to Multi-Objective Problems
Jul 13, 2026Simone Drago, Marco Mussi, Leonardo Bianconi +1Pairwise Preference Learning Pairwise Comparison
Politecnico di Milano, Milan, Italy
Attention Limited Reward Learning
Jul 6, 2026Wenqian XingPairwise Preference Learning Reward Modeling
Management Science and Engineering Department, Stanford University
Reasoning Arena: Trace Tournaments When Verifiable Rewards Fall Short
Jun 8, 2026Han Zhou, Adam X. Yang, Laurence Aitchison +2Pairwise Preference Learning Reward Modeling
University of Cambridge · 2Mistral AI · *Work done as an AI Scientist Intern at Mistral AI.
Bradley-Terry Rankings for Recommender Systems Across Dataset Taxonomies
Jun 5, 2026Ekaterina Grishina, Stepan Kuznetsov, Askar Tsyganov +8Algorithm Selection Pairwise Comparison
HSE University Moscow, Russian Federation
Rethinking Sales Lead Scoring with LLM-based Hierarchical Preference Ranking
Jun 3, 2026Chenyu Zhang, Yiwen Liu, Yin Sun +4Learning to Rank LLM Reranking
Intelligent Business Team, Li Auto Inc.
Reward Learning from Best-of- $N$ Preference Data: Targets, Tradeoffs, and Design Principles
May 28, 2026Rattana Pukdee, Maria-Florina Balcan, Pradeep RavikumarPairwise Preference Learning Reward Modeling
Machine Learning Department Carnegie Mellon University
Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries
May 22, 2026Dongmin Lee, Anuran Makur, Japneet SinghLearning to Rank Pairwise Ranking
Department of Computer Science Purdue University West Lafayette, IN, USA · Department of Computer Science Elmore Family School of Electrical and Computer Engineering Purdue University West Lafayette, IN, USA
Operationalizing Individual Fairness via Gradient Descent and Bradley-Terry Models
May 22, 2026Conlan Olson, Linjun Zhang, Zhun Deng +1Mahalanobis Distance Algorithmic Fairness
Columbia University · Rutgers University · UNC Chapel Hill +1
A Unified Perturbation Framework for Analyzing Leaderboard Stability and Manipulation
May 15, 2026Hosna Oyarhoseini, Jimmy Lin, Amir-Hossein KarimiLLM Evaluation Learning to Rank
University of Waterloo, Waterloo, Ontario, Canada.
OpenDeepThink: Parallel Reasoning via Bradley-Terry Aggregation
May 14, 2026Shang Zhou, Wenhao Chai, Kaiyuan Liu +3Pairwise Comparison Test-Time Optimization
1UC San Diego · 2Princeton University · University of Washington +1
Variance-aware Reward Modeling with Anchor Guidance
May 12, 2026Shuxing Fang, Ruijian Han, Liangyu Zhang +1Pairwise Preference Learning Reward Modeling
Department of Data Science and Artificial Intelligence, Hong Kong Polytechnic University · School of Statistics and Data Science, Shanghai University of Finance and Economics
On rankings in multiplayer games with an application to the game of Whist
Apr 1, 2026Alexis Coyette, Charles Modera, Candy Sonveaux +14Bradley–Terry Model Game Theory
Department of Mathematics, Naxys, Unamur, Belgium · Department of Physics and Astronomy, CSDC, University of Florence, Italy
Who can we trust? LLM-as-a-jury for Comparative Assessment
Feb 18, 2026Mengjie Qian, Guangzhi Sun, Mark J. F. Gales +1LLM-as-a-Judge Language Model Generation Evaluation
Department of Engineering, University of Cambridge, UK.
Dropping Just a Handful of Preferences Can Change Top Large Language Model Rankings
Aug 16, 2025Jenny Y. Huang, Yunyi Shen, Dennis Wei +1Pairwise Preference Learning LLM Evaluation
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology · MIT-IBM Watson AI Lab · IBM Research

Oct 21, 2026J/K move · Enter open · S save

Alternative Strategies for Active Learning with Bayesian Bradley Terry Model

Saman Jayasinghe, Sean Walton, Alma Rahat, Andy Gray+1

Swansea University, United Kingdom · Loughborough University, United Kingdom · Bath Spa University, United Kingdom+1

Pairwise Ranking Active Preference Learning Bradley–Terry Model Bayesian Inference

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Comparative judgement uses pairwise comparisons to rank items, but recovering accurate rankings from a limited number of judgements depends on both the inference method and the pairs selected. We developed a Bayesian Bradley-Terry model (BBTM) that uses Polya-Gamma data augmentation for efficient Gibbs sampling and quantifies uncertainty in latent abilities and ranks. We propose three active learning strategies based on the knowledge gradient (KG) principle. We define our acquisition functions using Kendall's tau distance, posterior rank entropy, and posterior separation. Approximate one-step updates to posterior moments reduce the computational cost of evaluating candidate pairs. We also introduce Posterior Separation Reliability (PSR), which measures the spread of posterior mean abilities relative to posterior uncertainty. It provides an internal indicator of ranking reliability without requiring a reference ranking. In synthetic experiments covering different item counts, comparison budgets, and noise levels, BBTM generally recovers ranking more accurately than preference-based Bayesian comparative judgement (PBCJ). At low to moderate noise levels, the pairwise entropy pair selection strategy performs best in ranking recovery. However, at the highest noise levels, the KG strategy based on posterior separation produces better point rankings. PSR increases alongside improvements in ranking accuracy as comparisons accumulate. Robustness experiments identify the proportion of informative outcomes needed to meet specified accuracy targets within a fixed comparison budget. In a moderate noise setting, replacing 30% of outcomes with random choices has little effect on ranking performance. These findings demonstrate the value of Bayesian inference and active learning pair selection for recovering ranks from limited, noisy paired comparisons.