Performance unfairness of large language models in cross-language fact-checking

• Scalable computable evaluation system for LLM performance in fact-checking. • Inequality quantification across languages. • Checking-worthiness scoring and checking-authenticity verification. • Prompts in different types of language combination with different effects. • Role-restricted prompt engineering and model fine-tuning alleviate unfairness. Large language models (LLMs) are increasingly used for automated fact-checking, yet their performance often varies across languages, raising global fairness concerns. This study evaluated cross-language inequality in LLM-based fact-checking using 4,500 claims spanning nine languages across six language families. Besides building a systematic performance-evaluation pipeline covering instruction following, authenticity classification, evidence generation, and checking-worthiness scoring, we quantified inequality using standard deviation, coefficient of variation, Gini coefficient, and Theil index. Results showed substantial cross-language disparities, with higher performance on claims from rich-resource languages. To mitigate inequality, we tested two interventions, role-restricted prompt engineering and model fine-tuning. Both approaches reduced disparities, with fine-tuning achieving the largest and most consistent improvement across languages, particularly in checking-worthiness scoring. This study provides a reproducible framework for quantifying multilingual performance and fairness in LLM-based fact-checking and offers practical guidance for developing more equitable verification systems across diverse linguistic contexts.