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).
Figures & tables
Figure 1: Example of selection bias in discrete-choice settings: swapping the order of answers changes only non-semantic factors.
Figure 2: Comparison between Standard GRPO (left) and the proposed PA-GRPO (right). Standard GRPO treats permuted prompts as independent samples, suffering from permutation blindness where inconsistency goes unpunished. In contrast, PA-GRPO organizes samples into Permutation Groups. It introduces (1) a Cross-Permutation Advantage (using the permutation group mean as a baseline) and (2) a Consistency-Aware Reward to explicitly enforce semantic invariance across different permutations of the same instance.
LLM-as-a-Judge
Multiple Choice Questions
Model
Method
MT-Bench
JudgeBench
PreferenceBench
RewardBench
GPQA
ARC-Challenge
TinyMMLU
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Llama-3.1-8B
Base
59.6
25.2
22.2
35.0
34.8
6.1
60.8
22.6
22.1
60.5
31.5
26.2
27.3
40.0
27.2
73.0
82.5
78.9
54.2
68.9
57.0
GRPO
75.7
80.6
65.4
48.2
56.1
28.2
82.2
85.1
76.3
70.9
76.9
61.5
29.5
55.6
29.7
89.0
92.1
91.5
67.3
77.9
73.0
UniBias
68.5
59.4
48.2
50.2
23.0
10.9
79.7
65.6
62.5
68.4
64.4
50.6
32.3
56.1
31.8
80.4
90.0
83.6
61.1
76.5
65.0
PriDe
65.6
46.2
38.9
49.1
16.2
7.2
81.6
69.1
66.2
65.1
52.8
41.5
31.0
49.1
27.4
79.1
83.0
79.0
59.7
69.5
58.0
Table 1: Main results on Llama-3.1-8B-Instruct, Qwen3-8B, and Qwen3-32B across 7 benchmarks. All scores are rounded to one decimal place. PA-GRPO results show the absolute score (top) and the gain/drop compared to the best baseline (bottom). Bold indicates the best result in each column.
LLM-as-a-Judge
Multiple Choice Questions
Method
MT-Bench
JudgeBench
PreferenceBench
RewardBench
GPQA
ARC-Challenge
TinyMMLU
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Base
59.6
25.2
22.2
35.0
34.8
6.1
60.8
22.6
22.1
60.5
31.5
26.2
27.3
40.0
27.2
73.0
82.5
78.9
54.2
68.9
57.0
GRPO
75.7
80.6
65.4
48.2
56.1
28.2
82.2
85.1
76.3
70.9
76.9
61.5
29.5
55.6
29.7
89.0
92.1
91.5
67.3
77.9
73.0
+ rcon
75.2
83.1
66.5
48.0
56.5
29.2
82.6
85.9
76.9
70.6
79.0
61.9
29.9
56.4
31.0
87.8
92.3
92.0
67.1
78.8
73.0
+ APA
76.6
84.2
67.8
49.3
55.4
30.5
83.4
86.4
77.8
69.8
78.7
61.1
30.7
57.1
32.2
89.7
92.3
91.9
67.5
79.4
74.0
Table 2: Ablation study on Llama-3.1-8B-Instruct across all 7 benchmarks. We group datasets into LLM-as-a-Judge tasks and MCQ tasks. The best results are bolded . Adding both components ( APA and rcon ) consistently yields the best robustness.
LLM-as-a-Judge
Multiple Choice Questions
Setting
MT-Bench
JudgeBench
PreferenceBench
RewardBench
GPQA
ARC-Challenge
TinyMMLU
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Base
59.6
25.2
22.2
35.0
34.8
6.1
60.8
22.6
22.1
60.5
31.5
26.2
27.3
40.0
27.2
73.0
82.5
78.9
54.2
68.9
57.0
λ=0.5
78.0
86.4
69.8
56.5
55.4
31.9
85.3
86.8
78.9
70.7
80.9
60.5
32.1
56.6
32.0
89.4
92.0
92.4
67.1
78.2
74.0
λ=1.0 (Default)
77.6
88.0
71.7
57.1
58.3
32.4
86.2
87.2
79.8
71.0
82.7
62.3
32.1
57.2
33.2
89.3
92.9
92.6
67.9
81.9
75.0
λ=2.0
76.5
88.6
70.5
56.8
55.9
32.0
85.0
87.5
79.1
70.3
82.5
62.1
31.4
58.0
33.6
88.7
91.2
91.1
66.4
80.1
73.0
Table 3: Impact of the consistency reward coefficient ( λ ) on Llama-3.1-8B-Instruct. We group datasets into LLM-as-a-Judge tasks and MCQ tasks. λ=1.0 achieves the best balance. The best results are bolded .
Figure 3: Impact of Permutation Group Size ( P ).
LLM-as-a-Judge
Multiple Choice Questions
Method
MT-Bench
JudgeBench
PreferenceBench
RewardBench
GPQA
ARC-Challenge
TinyMMLU
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Base (Direct)
59.6
25.2
22.2
35.0
34.8
6.1
60.8
22.6
22.1
60.5
31.5
26.2
27.3
40.0
27.2
73.0
82.5
78.9
54.2
68.9
57.0
Base (CoT)
68.7
68.2
58.0
39.0
48.5
17.1
70.3
61.3
58.1
67.5
76.2
54.8
24.5
53.9
26.6
84.6
84.2
81.1
62.4
74.3
64.0
PA-GRPO (Direct)
75.1
85.5
69.3
58.0
54.5
31.8
84.8
82.3
75.9
69.5
80.1
59.8
31.0
54.1
30.8
86.5
89.9
88.7
66.5
77.9
72.0
PA-GRPO (CoT)
77.6
88.0
71.7
57.1
58.3
32.4
86.2
87.2
79.8
71.0
82.7
62.3
32.1
57.2
33.2
89.3
92.9
92.6
67.9
81.9
75.0
Table 4: Performance comparison of Direct vs. Chain-of-Thought (CoT) inference strategies. We report Accuracy, Consistency, and Consistent Accuracy for both the Base model and PA-GRPO across seven benchmarks.
LLM-as-a-Judge
Multiple Choice Questions
Bias Setting
MT-Bench
JudgeBench
PreferenceBench
RewardBench
GPQA
ARC-Challenge
TinyMMLU
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Acc
Con
CA
Label Bias (Label-only)
76.7
92.2
72.8
56.3
79.0
45.8
74.9
62.8
56.2
70.7
87.5
64.4
22.0
67.2
20.8
80.7
95.6
81.3
63.5
83.8
66.0
Position Bias (Order-only)
77.4
85.1
69.9
55.0
45.5
27.7
74.2
66.9
57.7
71.6
82.0
62.6
27.9
65.0
27.7
80.9
91.9
82.8
64.3
80.5
72.0
Selection Bias (Standard)
77.6
88.0
71.7
57.1
58.3
32.4
86.2
87.2
79.8
71.0
82.7
62.3
32.1
57.2
33.2
89.3
92.9
92.6
67.9
81.9
75.0
Table 5: Bias decomposition results under three controlled protocols: Label Bias, Position Bias, and Selection Bias. We report Accuracy, Consistency, and Consistent Accuracy for PA-GRPO across seven benchmarks.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
LLM-as-a-Judge
Multiple Choice Questions
Method / Setting
MT-Bench
JudgeBench
PreferenceBench
RewardBench
GPQA
ARC-Challenge
TinyMMLU
RStd
CKLD
RStd
CKLD
RStd
CKLD
RStd
CKLD
RStd
CKLD
RStd
CKLD
RStd
CKLD
Base
0.364
0.378
0.216
0.627
0.386
0.453
0.331
0.291
0.056
1.570
0.025
0.005
0.033
0.028
GRPO
0.036
0.010
0.060
0.156
0.057
0.009
0.024
0.006
0.042
1.331
0.019
0.001
0.026
0.030
UniBias
0.047
0.005
0.050
0.019
0.066
0.008
0.184
0.380
0.044
1.129
0.015
0.003
0.027
0.019
PriDe
0.078
0.012
0.107
0.023
0.051
0.006
0.029
0.002
0.036
0.983
0.014
0.002
0.029
0.031
Appendix
Table 6: Bias evaluation results using RStd and CKLD (lower is better) on Llama-3.1-8B-Instruct across all seven benchmarks. All rows use the default evaluation prompt unless otherwise noted. The final row reports PA-GRPO under the rewritten prompt shown below. Bold indicates the best (lowest) result among all compared settings.
Bias has long been studied in social psychology and cognitive science, where decades of research have produced a body of validated interventions that reduce stereotypical thinking and prejudiced responses in humans. We propose Debias It Yourself (DIY), a cognitively grounded framework that translates five such interventions into debiasing procedures for large language models and delivers them through three established paradigms: Show (in-context examples), Train (instruction tuning), and Revise (guided self-revision). Across three models, five bias benchmarks, eleven debiasing baselines, and three reasoning benchmarks, Train+Revise and Revise alone attain the top two average ranks, lead the bias-reasoning tradeoff (mean bias as low as 2% at 90% reasoning accuracy), and reduce bias on unseen dimensions by up to 14.8%. Our code and data are publicly available.
Chahat Raj, Sina Mansouri, Aylin Caliskan +2
George Mason University · University of Washington
Mitigating social bias in Large Language Models (LLMs) presents a distinct alignment challenge: unlike verifiable tasks, bias lacks a single ground truth, creating a high-variance, subjective reward landscape. Previous preference-based fine-tuning methods have major trade-offs: Direct Preference Optimization (DPO) is limited by the lack of exploration inherent in offline training, while Proximal Policy Optimization (PPO) can lead to training instability due to potentially unreliable critic estimates. In this paper, we propose BiasGRPO, a framework using Group Relative Policy Optimization (GRPO) to stabilize alignment by normalizing rewards across a group of sampled completions. By substituting the value function with a group-relative baseline, our approach reduces instability while maintaining the exploration benefits of online training. We find that BiasGRPO outperforms DPO and PPO across multiple benchmarks, indicating its effectiveness. To adapt GRPO, we synthetically extend a dataset spanning multiple domains and contexts. We also create and release a custom bias reward model that effectively guides generation while being highly compute-efficient and avoiding knowledge degradation, providing a valuable resource that can be seamlessly integrated into multi-objective RLHF pipelines.
Large language models pick up social biases from the data they are trained on and carry those biases into downstream applications, often reinforcing stereotypes around gender, race, religion, disability, age, and socioeconomic status. The standard fixes (retraining on curated data or fine-tuning with human feedback) are expensive, need access to model weights, and risk degrading the model on other tasks. In this paper we take a different route: we debias the model at decoding time, treating bias mitigation as a structured search over candidate tokens without ever touching model weights. A separate Process Reward Model (PRM) acts as a judge, scoring each candidate for both fairness and fluency. We design three schemes of increasing sophistication (Best-of-N selection, Sequential critique-and-revise, and Constitutional self-audit) and evaluate them on four models (GPT-4o-mini, Llama 3.2 3B, Gemma 3 4B, Qwen 2.5 3B) across a 200-prompt bilingual benchmark in English and Urdu covering eight bias categories. Sequential debiasing proves the most effective, raising mean bias scores by up to +0.40 over baseline while preserving (and sometimes improving) fluency. We then extend all three schemes to open-ended generation, where each token is debiased on the fly, and introduce a lightweight Bias Guard gate that fires only on potentially biased words, keeping overhead near 2x for well-calibrated models. A formal overhead metric that separates generator cost from judge cost reveals that Best-of-N is effectively free on the generator side in a native implementation. GPT-4o-mini, included as a strong proprietary anchor, confirms that the framework scales with model capability; the three open-weight models show where current small-scale LLMs still struggle.