Bradley–Terry Model

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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.
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
Generalizing Preference-based Reinforcement Learning: a Rationality Model for Incomparability
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
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

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How Many Repeated Pairwise Comparisons Are Needed for Ranking under Heterogeneity?

Shashaank Aiyer, Han Shao

University of Maryland

Pairwise Ranking Pairwise Preference Learning Sample Complexity Bradley–Terry Model

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We study ranking models by population-average utility from pairwise comparisons when preferences vary across users and tasks. Prior work shows that a single comparison per user can be insufficient to identify the alternative with the highest average utility, even with arbitrarily many users (Golz et al., 2025). We investigate how many repeated comparisons within each user-task context are necessary and sufficient for ranking recovery. Under a heterogeneous Bradley-Terry model with fixed inverse temperature, we start with a naive MLE-based algorithm that requires

Ω(1/Δ^2)

repeated comparisons per context to ensure ranking recovery. We then present two MLE-based variants and a randomized Russian Roulette-style algorithm that recover the ranking using

O(\log(1/Δ))

repeated comparisons per context, and we prove that this logarithmic dependence is optimal. Despite this worst-case requirement, our Russian Roulette algorithm uses only

O(1)

comparisons per context in expectation. Synthetic experiments and semi-synthetic experiments based on Arena data compare the four algorithms in settings with varying levels of preference heterogeneity and under varying context distributions.

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