EIP: Weighted Ranking of LLMs by Quantifying Question Difficulty

Benchmarks establish a standardized evaluation framework to systematically assess the performance of large language models (LLMs), facilitating objective comparisons and driving advancements in the field. However, existing benchmarks fail to differentiate question difficulty, limiting their ability to effectively distinguish models' capabilities. To address this limitation, we propose Empirical Interaction Propagation (EIP), a novel framework designed to quantify both question difficulty and model competency. EIP introduces difficulty as the primary criterion for differentiation, enabling a more fine-grained evaluation of LLM capabilities. EIP's core mechanism facilitates bidirectional score propagation between models and questions. The core intuition of EIP is that a model earns a competency score when it correctly answers a question, while a question's difficulty score increases when it challenges a model. Using this framework, we evaluate 30 models on 35,550 questions across multiple domains. EIP achieves 90\% agreement with human judgments and consistently outperforms strong baselines such as IRT. It also exhibits strong stability, fast convergence, and high computational efficiency, making it a practical solution for large-scale, difficulty-aware LLM evaluation. Code is available at https://github.com/Leozz04/EIP.