A Statistical Framework for Ranking LLM-based Chatbots
Keywords: Large Language Models (LLMs), Paired Comparison, Statistical Ranking, Human Preferences, Chatbot Arena, Logistic Regression
TL;DR: We introduce a rigorous statistical framework for ranking large language models (LLMs) using crowdsourced comparisons, improving accuracy for ties, wins, and losses beyond current methods like Elo.
Abstract: Large language models (LLMs) have transformed natural language processing, with frameworks like Chatbot Arena providing pioneering platforms for evaluating these models. By facilitating millions of pairwise comparisons based on human judgments, Chatbot Arena has become a cornerstone in LLM evaluation, offering rich datasets for ranking models in open-ended conversational tasks. Building upon this foundation, we propose a statistical framework that incorporates key advancements to address specific challenges in pairwise comparison analysis. First, we introduce a factored tie model that enhances the ability to handle ties—an integral aspect of human-judged comparisons—significantly improving the model’s fit to observed data. Second, we extend the framework to model covariance between competitors, enabling deeper insights into performance relationships and facilitating intuitive groupings into performance tiers. Third, we resolve optimization challenges arising from parameter invariances by introducing novel constraints, ensuring stable and interpretable parameter estimation. Through rigorous evaluation and extensive experimentation, our framework demonstrates substantial improvements over existing methods in modeling pairwise comparison data. To support reproducibility and practical adoption, we release leaderbot, an open-source Python package implementing our models and analyses.
Primary Area: foundation or frontier models, including LLMs
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Submission Number: 13986
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