Prompt-Dependent Ranking of Large Language Models with Uncertainty Quantification

TL;DR

This paper introduces a statistically rigorous framework for ranking large language models based on human preferences that accounts for uncertainty and prompt dependency, improving decision-making robustness.

Contribution

It develops a novel method for prompt-dependent ranking inference with valid uncertainty quantification, moving beyond fixed point estimates of model utilities.

Findings

Rankings vary significantly across different prompts.

Many apparent rank differences are not statistically significant.

Uncertainty-aware rankings prevent misleading conclusions by acknowledging data limitations.

Abstract

Rankings derived from pairwise comparisons are central to many economic and computational systems. In the context of large language models (LLMs), rankings are typically constructed from human preference data and presented as leaderboards that guide deployment decisions. However, existing approaches rely on point estimates, implicitly treating rankings as fixed objects despite substantial estimation noise and context-dependent performance variation. Acting on such rankings can lead to misallocation and welfare loss when apparent differences are not statistically meaningful. We study prompt-dependent ranking inference under pairwise human preferences and develop a framework for decision-safe rankings with statistically valid uncertainty guarantees. We model preferences using a contextual Bradley-Terry-Luce model in which the latent utility of each model depends on the input prompt. Rather than targeting point estimates of utilities, we directly conduct inference on induced rankings, constructing confidence sets based on simultaneous confidence intervals for pairwise utility differences. This approach yields statistically valid marginal and simultaneous confidence sets for prompt-specific ranks. Our framework connects recent advances in rank inference to contextual preference learning and provides tools for robust ranking-based decision-making. Empirically, using large-scale human preference data from LLM evaluations, we show that rankings vary substantially across prompt characteristics and that many apparent rank differences are not statistically distinguishable. We further demonstrate how uncertainty-aware rankings identify dominance only when supported by the data and otherwise return partial orders.