💻 computer science

Quantifying and Mitigating Gender Bias in Legal Large Language Models:A Counterfactual Fairness Framework

This paper audits legal large language models for gender bias in China's wrongful-dismissal compensation calculations, revealing that counterfactual instability rather than directional bias is the primary failure mode, and proposes two effective remedies—Counterfactual Symmetric Calibration and Fairness-Constrained Fine-Tuning—to mitigate these errors by addressing missing formula knowledge.

Original authors: Yikuan Feng, Xiao Li

Published 2026-08-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yikuan Feng, Xiao Li

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are walking into a giant, high-tech library where the librarians are super-smart robots. These robots have read almost every book ever written and can answer questions about anything from cooking recipes to space travel. But there's a catch: sometimes, when you ask them a question, they might give you a different answer just because you changed one tiny detail about yourself, like your name or your gender. This is a big deal in the world of "Artificial Intelligence" (AI), specifically in a field called "Machine Learning." Think of these AI models as digital brains that learn patterns from data. One of the biggest worries for scientists and lawyers is "bias." Bias is like a pair of tinted glasses; if the AI wears glasses that make it see men differently than women, it might make unfair decisions. Usually, we worry about the AI being consistently unfair—like always giving men better answers than women. But what if the AI isn't consistently unfair, but just randomly confused? What if it gives you a great answer one day and a terrible one the next, just because you swapped a word in your question? That's the mystery this paper tries to solve.

The researchers in this study decided to put four of the world's most popular "Legal Large Language Models" (think of them as super-lawyer robots) to the test. They chose a very specific, math-heavy job: calculating how much money a worker should get if they are fired unfairly in China. The law here is like a strict recipe: if you worked for 5 years and earned $1,000 a month, the robot must calculate exactly $10,000. There is no room for guessing. If the robot says $12,000, it's wrong. If it says $8,000, it's also wrong. The scientists created 50 different "what-if" stories. In each story, they asked the robot to calculate the payout for a man, and then asked the exact same question again, but changed the worker's gender to a woman. They did this 400 times in total.

Here is the surprising twist they found. They expected the robots to be consistently biased, like a scale that always tips too far to the left. Instead, they found something much stranger: instability. The robots weren't consistently favoring men or women. Instead, they were acting like a jittery calculator. For most of the stories, the robots gave the exact same answer for both men and women. But for a few specific stories, the robots went crazy. They would give a man a huge payout and the woman a tiny one, or vice versa, with no pattern to explain why. It was like a coin flip that sometimes landed on heads, sometimes on tails, and sometimes on the edge. The researchers call this "counterfactual instability." It's a scary kind of unfairness because you can't just fix it by adding a "correction factor" to the robot's brain. If the robot is randomly wrong, you can't predict when it will mess up.

To fix this, the team tried two different "band-aids." The first one was a clever trick called Counterfactual Symmetric Calibration (CSC). Imagine you have a robot that sometimes gives you the wrong answer. Instead of trying to retrain the robot (which is hard and expensive), you just put a safety net under it. Every time the robot gives a different answer for a man and a woman, you ignore the robot and just use the math formula from the law book instead. This worked amazingly well. For some robots, it fixed the legal accuracy by as much as 72 percentage points! It was like catching a falling plate before it hits the floor.

The second fix was a deeper surgery called Fairness-Constrained Fine-Tuning (FCFT). Here, the researchers took a smaller robot and taught it the math formula directly, while also telling it, "Hey, make sure you treat men and women exactly the same." They discovered something very important: the robots weren't being mean or sexist on purpose. They were just bad at math! The main reason they gave wrong answers was that they didn't actually know the formula inside the law book. Once they were taught the formula, the "gender bias" mostly disappeared. It turns out the robots weren't wearing tinted glasses; they just didn't know how to do the addition.

In the end, this paper tells us that when we use AI for legal decisions, we can't just trust it to "talk" like a lawyer. If the law is a math problem, the AI needs to act like a calculator, not a storyteller. The biggest danger isn't that the AI hates a certain group of people; it's that it might be unpredictably confused. The good news is that we can build safety nets to catch those mistakes, and we can teach the robots the rules so they stop guessing. It's a reminder that in the world of AI, sometimes the most important thing isn't how smart the robot sounds, but whether it can do simple math without tripping over its own feet.

Technical Summary: Quantifying and Mitigating Gender Bias in Legal Large Language Models

1. Problem Statement

The paper addresses the critical issue of algorithmic bias in legal Large Language Models (LLMs), specifically focusing on gender bias within the context of wrongful-dismissal compensation under Article 87 of China's Labour Contract Law (LCL). Unlike common-law systems where outcomes are probabilistic (e.g., recidivism risk), this domain offers a unique "clean" experimental testbed: the fair compensation amount is uniquely determined by a statutory formula ( $Compensation = Tenure \times Monthly\ Salary \times 2$ ).

The authors argue that existing bias research often overlooks a specific failure mode: counterfactual instability. While prior work focuses on directional bias (e.g., systematically favoring one gender), this study investigates whether a single-token gender substitution in an otherwise identical prompt causes unpredictable, case-specific deviations in the recommended compensation amount. Such instability violates counterfactual fairness (Kusner et al., 2017) and undermines procedural justice, as it introduces "technical arbitrariness" where legally irrelevant attributes (gender) unpredictably alter outcomes.

2. Methodology

2.1 Counterfactual Fairness Framework

The study defines gender bias using the Bias Shift Rate ( $\Delta$ ):
$\Delta = \frac{R_{male} - R_{female}}{\bar{R}}$
Where $R_{male}$ and $R_{female}$ are the compensation amounts recommended for identical scenarios differing only in the plaintiff's gender, and $\bar{R}$ is their average.

Ground Truth ( $R^*$ ): The statutory value calculated via the LCL formula.
Legal Compliance: An output is compliant if it falls within $\pm 10\%$ of $R^*$ .
Bias Threshold: A scenario is considered biased if $|\Delta| > 0.05$ .

2.2 Experimental Design

Scenarios: 50 counterfactual scenario pairs were constructed, varying tenure (1–12 years), salary (4k–30k CNY), and including legally irrelevant context (education, family status) to simulate realistic noise.
Models: Four mainstream LLMs were evaluated via their official APIs:
- Qwen 3.6 Plus (Alibaba)
- DeepSeek V4 Flash (DeepSeek)
- Gemini 3.1 Flash Lite (Google)
- Claude Sonnet 4.6 (Anthropic)
Inference Protocol: 400 deterministic inferences ( $K=1$ , temperature $= 0$ ) were performed. This design isolates deterministic sensitivity to the gender token, excluding sampling variance.

2.3 Remediation Strategies

Two complementary strategies were proposed and tested:

Counterfactual Symmetric Calibration (CSC): A post-processing safety net for closed-source models. If $|\Delta| > 0.05$ , both gendered outputs are replaced by the statutory value $R^*$ . This requires no model retraining.
Fairness-Constrained Fine-Tuning (FCFT): A parameter-level approach for open-source models (tested on Qwen1.5-1.8B-Chat). The training objective combines standard language loss with a fairness regularizer:
$L_{total} = L_{LM} + \lambda \cdot L_{fairness}$
Where $L_{fairness}$ penalizes the KL divergence between gender-conditioned output distributions. An ablation study compared four variants: Baseline, Data Alignment only, KL Loss only, and Full FCFT.

3. Key Results

3.1 Bias Detection: Instability over Direction

Across all four models, the study found no statistically significant directional bias (all Wilcoxon $p > 0.28$ ). However, all models exhibited pronounced counterfactual instability:

DeepSeek V4 Flash: Lowest instability (Mean $|\Delta| = 0.082$ ), with 86% of scenarios showing identical recommendations.
Qwen 3.6 Plus & Claude Sonnet 4.6: Highest instability (Mean $|\Delta| = 0.266$ and $0.214$ respectively), with 74% of scenarios showing bias.
Distribution: The distribution of $|\Delta|$ is heavy-tailed. While the median deviation for some models was zero, a minority of cases produced extreme deviations, indicating that errors are sporadic and unpredictable rather than uniform.

3.2 Legal Compliance

DeepSeek achieved the highest baseline legal compliance (78%).
Claude and Gemini showed systematic negative deviations from the statutory formula even in gender-neutral scenarios, resulting in very low baseline compliance (2% and 6%, respectively).
Finding: High fluency and professional wording (as seen in Claude's outputs) do not correlate with legal accuracy.

3.3 Effectiveness of Remediation

CSC Performance: Applying CSC dramatically improved legal compliance:
- Qwen: +60 percentage points (34% $\to$ 94%).
- Claude: +72 percentage points (2% $\to$ 74%).
- DeepSeek: +14 percentage points (78% $\to$ 92%).
- The method successfully eliminated bias in triggered scenarios ( $\Delta \to 0$ ).
FCFT Ablation: The diagnostic fine-tuning revealed that missing formula knowledge, not encoded gender preference, is the primary driver of bias.
- Variant B (Data Alignment only): Achieved 97.29% legal accuracy and the lowest $|\Delta|$ (0.0213), proving that supplying statutory labels resolves most issues.
- Variant D (Full FCFT): Further reduced KL divergence (0.0010) but at a slight cost to accuracy compared to Variant B, suggesting the fairness regularizer acts as a smoothing constraint.

4. Significance and Claims

The paper claims three primary contributions:

First Large-Scale Counterfactual Audit: It provides the first systematic audit of legal LLMs in a civil-law, formula-determined setting, characterizing counterfactual instability as the dominant bias form, distinct from directional discrimination.
Remediation Pipeline: It validates CSC as a low-cost, high-impact safety net for closed-source APIs and FCFT as a diagnostic tool for open-source models.
Architectural Insight: The results argue for decoupling legal calculation from language generation. Since the ground truth is a deterministic function, entrusting numerical computation to generative models introduces unnecessary variance. The authors propose a neuro-symbolic architecture where symbolic modules handle formula execution, and LLMs handle context and explanation.

The authors emphasize that this form of bias (inconsistency) is invisible to aggregate group-level audits and cannot be corrected by scalar adjustments, necessitating individual-level counterfactual testing. They conclude that for formula-determined legal tasks, regulatory standards should mandate counterfactual fairness audits and the integration of formula-execution modules to ensure procedural justice.