# Theoretical Tensions in RLHF: Reconciling Empirical Success with Inconsistencies in Social Choice Theory

arXiv: https://arxiv.org/abs/2506.12350 · HTML: https://mlsanity.com/paper/2506.12350/

## Key facts

- Cited by 7 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 40 of its 55 references that are in the map.
- First posted on arXiv 14 Jun 2025.

## 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 40)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Statistical Rejection Sampling Improves Preference Optimization](https://mlsanity.com/paper/2309.06657/) (2023)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [From r to Q^*: Your Language Model is Secretly a Q-Function](https://mlsanity.com/paper/2404.12358/) (2024)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models](https://mlsanity.com/paper/2310.10505/) (2023)
- [Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data](https://mlsanity.com/paper/2404.14367/) (2024)
- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [HelpSteer: Multi-attribute Helpfulness Dataset for SteerLM](https://mlsanity.com/paper/2311.09528/) (2023)
- [Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF](https://mlsanity.com/paper/2312.08358/) (2023)
- [Understanding the performance gap between online and offline alignment algorithms](https://mlsanity.com/paper/2405.08448/) (2024)
- [RLHF from Heterogeneous Feedback via Personalization and Preference Aggregation](https://mlsanity.com/paper/2405.00254/) (2024)
- [On the Algorithmic Bias of Aligning Large Language Models with RLHF: Preference Collapse and Matching Regularization](https://mlsanity.com/paper/2405.16455/) (2024)
- [Preserving Diversity in Supervised Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2408.16673/) (2024)
- [Learn Your Reference Model for Real Good Alignment](https://mlsanity.com/paper/2404.09656/) (2024)
- [Online Iterative Reinforcement Learning from Human Feedback with General Preference Model](https://mlsanity.com/paper/2402.07314/) (2024)
- [Axioms for AI Alignment from Human Feedback](https://mlsanity.com/paper/2405.14758/) (2024)
- [Asymptotics of Language Model Alignment](https://mlsanity.com/paper/2404.01730/) (2024)
- [Dataset Reset Policy Optimization for RLHF](https://mlsanity.com/paper/2404.08495/) (2024)
- [AI Alignment and Social Choice: Fundamental Limitations and Policy Implications](https://mlsanity.com/paper/2310.16048/) (2023)

## Built on by (most cited first, 7 of 7)

- [How Sampling Shapes LLM Alignment: From One-Shot Optima to Iterative Dynamics](https://mlsanity.com/paper/2602.12180/) (2026)
- [AI Alignment From Social Choice Perspectives](https://mlsanity.com/paper/2606.21550/) (2026)
- [The Representation-Rationalizability Tradeoff in Reward Learning](https://mlsanity.com/paper/2606.00291/) (2026)
- [Asymptotic Universal Alignment: A New Alignment Framework via Test-Time Scaling](https://mlsanity.com/paper/2601.08777/) (2026)
- [Back to Blackwell: Closing the Loop on Intransitivity in Multi-Objective Preference Fine-Tuning](https://mlsanity.com/paper/2602.19041/) (2026)
- [Beyond Post-Hoc Temperature Scaling: Bilevel Optimization for LLM Calibration](https://mlsanity.com/paper/2608.07419/) (2026)
- [Axiom Satisfiability of Linear Rewards in Alignment](https://mlsanity.com/paper/2610.06892/) (2026)

## Abstract (arXiv)

Despite its empirical success, Reinforcement Learning from Human Feedback (RLHF) has been shown to violate almost all the fundamental axioms in social choice theory -- such as majority consistency, pairwise majority consistency, and Condorcet consistency. This raises a foundational question: why does RLHF perform so well in practice if it fails these seemingly essential properties? In this paper, we resolve this paradox by showing that under mild and empirically plausible assumptions on the preference profile, RLHF does satisfy pairwise majority and Condorcet consistency. These assumptions are frequently satisfied in real-world alignment tasks, offering a theoretical explanation for RLHF's strong practical performance. Furthermore, we show that a slight modification to the reward modeling objective can ensure pairwise majority or Condorcet consistency even under general preference profiles, thereby improving the alignment process. Finally, we go beyond classical axioms in economic and social choice theory and introduce new alignment criteria -- preference matching, preference equivalence, and group preference matching -- that better reflect the goal of learning distributions over responses. We show that while RLHF satisfies the first two properties, it fails to satisfy the third. We conclude by discussing how future alignment methods may be designed to satisfy all three.