# What Does Preference Learning Recover from Pairwise Comparison Data?

arXiv: https://arxiv.org/abs/2602.10286 · HTML: https://mlsanity.com/paper/2602.10286/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reward modeling and RLHF, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 39 of its 80 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Reward modeling and RLHF](https://mlsanity.com/alignment/reward-modeling-and-rlhf/)

## Builds on (most cited first, 30 of 39)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [Skywork-Reward-V2: Scaling Preference Data Curation via Human-AI Synergy](https://mlsanity.com/paper/2507.01352/) (2025)
- [RM-Bench: Benchmarking Reward Models of Language Models with Subtlety and Style](https://mlsanity.com/paper/2410.16184/) (2024)
- [Contextual Dueling Bandits](https://mlsanity.com/paper/1502.06362/) (2015)
- [Not All Rollouts are Useful: Down-Sampling Rollouts in LLM Reinforcement Learning](https://mlsanity.com/paper/2504.13818/) (2025)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)
- [Active Preference Optimization for Sample Efficient RLHF](https://mlsanity.com/paper/2402.10500/) (2024)
- [Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence](https://mlsanity.com/paper/1505.01462/) (2015)
- [RMB: Comprehensively Benchmarking Reward Models in LLM Alignment](https://mlsanity.com/paper/2410.09893/) (2024)
- [Preference Learning Algorithms Do Not Learn Preference Rankings](https://mlsanity.com/paper/2405.19534/) (2024)
- [Spectral MLE: Top-K Rank Aggregation from Pairwise Comparisons](https://mlsanity.com/paper/1504.07218/) (2015)
- [Sparse Dueling Bandits](https://mlsanity.com/paper/1502.00133/) (2015)
- [Uncertainty quantification in the Bradley-Terry-Luce model](https://mlsanity.com/paper/2110.03874/) (2021)
- [Beyond Bradley-Terry Models: A General Preference Model for Language Model Alignment](https://mlsanity.com/paper/2410.02197/) (2024)
- [Minimax-optimal Inference from Partial Rankings](https://mlsanity.com/paper/1406.5638/) (2014)

## Built on by (most cited first, 3 of 3)

- [Reward Learning from Best-of-N Preference Data: Targets, Tradeoffs, and Design Principles](https://mlsanity.com/paper/2605.30619/) (2026)
- [Sorting from Counterexamples](https://mlsanity.com/paper/2608.21579/) (2026)
- [Learning in Continuous Games from Pairwise Preference Feedback](https://mlsanity.com/paper/2610.05428/) (2026)

## Abstract (arXiv)

Pairwise preference learning is central to machine learning, with recent applications in aligning language models with human preferences. A typical dataset consists of triplets (x, y^+, y^-), where response y^+ is preferred over response y^- for context x. The Bradley--Terry (BT) model is the predominant approach, modeling preference probabilities as a function of latent score differences. Standard practice assumes data follows this model and learns the latent scores accordingly. However, real data may violate this assumption, and it remains unclear what BT learning recovers in such cases. Starting from triplet comparison data, we formalize the preference information it encodes through the conditional preference distribution (CPRD). We give precise conditions for when BT is appropriate for modeling the CPRD, and identify factors governing sample efficiency -- namely, margin and connectivity. Together, these results offer a data-centric foundation for understanding what preference learning actually recovers.