# Mitigating Selection Bias in Large Language Models via Permutation-Aware GRPO

arXiv: https://arxiv.org/abs/2603.21016 · HTML: https://mlsanity.com/paper/2603.21016/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 22 Mar 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 22 of 22)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Large Language Models Are Not Robust Multiple Choice Selectors](https://mlsanity.com/paper/2309.03882/) (2023)
- [Prometheus 2: An Open Source Language Model Specialized in Evaluating Other Language Models](https://mlsanity.com/paper/2405.01535/) (2024)
- [JudgeBench: A Benchmark for Evaluating LLM-based Judges](https://mlsanity.com/paper/2410.12784/) (2024)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Way Off-Policy Batch Deep Reinforcement Learning of Implicit Human Preferences in Dialog](https://mlsanity.com/paper/1907.00456/) (2019)
- [Judging the Judges: A Systematic Study of Position Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2406.07791/) (2024)
- [Surface Form Competition: Why the Highest Probability Answer Isn't Always Right](https://mlsanity.com/paper/2104.08315/) (2021)
- [Eliminating Position Bias of Language Models: A Mechanistic Approach](https://mlsanity.com/paper/2407.01100/) (2024)
- [Beyond Performance: Quantifying and Mitigating Label Bias in LLMs](https://mlsanity.com/paper/2405.02743/) (2024)
- [Rectifying Demonstration Shortcut in In-Context Learning](https://mlsanity.com/paper/2403.09488/) (2024)
- [RoToR: Towards More Reliable Responses for Order-Invariant Inputs](https://mlsanity.com/paper/2502.08662/) (2025)

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

- [Overwhelmed by Choice: Studying LLM Decision Making at Scale](https://mlsanity.com/paper/2609.32809/) (2026)
- [Evaluating Stochastic Collapse and Implicit Bias in Multimodal Large Language Models](https://mlsanity.com/paper/2606.05874/) (2026)
- [Equal Ranking Quality, Different Decisions: Measuring and Reducing Order Dependence in LLM Scorers](https://mlsanity.com/paper/2608.26762/) (2026)

## Abstract (arXiv)

Large language models (LLMs) used for multiple-choice and pairwise evaluation tasks often exhibit selection bias due to non-semantic factors like option positions and label symbols. Existing inference-time debiasing is costly and may harm reasoning, while pointwise training ignores that the same question should yield consistent answers across permutations. To address this issue, we propose Permutation-Aware Group Relative Policy Optimization (PA-GRPO), which mitigates selection bias by enforcing permutation-consistent semantic reasoning. PA-GRPO constructs a permutation group for each instance by generating multiple candidate permutations, and optimizes the model using two complementary mechanisms: (1) cross-permutation advantage, which computes advantages relative to the mean reward over all permutations of the same instance, and (2) consistency-aware reward, which encourages the model to produce consistent decisions across different permutations. Experimental results demonstrate that PA-GRPO outperforms strong baselines across seven benchmarks, substantially reducing selection bias while maintaining high overall performance. The code is available on github (https://github.com/ECNU-Text-Computing/PA-GRPO).