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Prompt-Dependent Ranking of Large Language Models with Uncertainty Quantification

arXiv:2603.03336v1 Announce Type: new 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 di

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Angel Rodrigo Avelar Menendez, Yufeng Liu, Xiaowu Dai · · 1 min read · 9 views
#cs.CL #cs.LG

arXiv:2603.03336v1 Announce Type: new 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.

Executive Summary

This article introduces a novel framework for prompt-dependent ranking of large language models (LLMs), addressing the limitations of existing approaches that rely on point estimates and ignore estimation noise and context-dependent performance variation. The proposed framework uses a contextual Bradley-Terry-Luce model to infer rankings from human preference data, constructing confidence sets based on simultaneous confidence intervals for pairwise utility differences. Empirical results demonstrate that rankings vary substantially across prompt characteristics and that many apparent rank differences are not statistically distinguishable. This research has significant implications for LLM evaluation and deployment, as it provides a decision-safe ranking approach with statistically valid uncertainty guarantees.

Key Points

  • ▸ Proposes a contextual Bradley-Terry-Luce model for prompt-dependent ranking inference
  • ▸ Develops a framework for decision-safe rankings with statistically valid uncertainty guarantees
  • ▸ Empirically demonstrates the importance of considering estimation noise and context-dependent performance variation

Merits

Strength in Methodological Innovation

The article introduces a novel and theoretically sound approach to ranking LLMs, leveraging advances in rank inference and contextual preference learning.

Practical Significance

The framework provides decision-makers with statistically valid uncertainty guarantees, enabling more informed deployment decisions and potential welfare gains.

Demerits

Limited Generalizability

The article focuses on LLM evaluation and deployment, and the proposed framework may require modifications to accommodate other applications or domains.

Computational Complexity

The framework involves constructing simultaneous confidence intervals for pairwise utility differences, which may be computationally intensive, especially for large-scale datasets.

Expert Commentary

This article makes a significant contribution to the field of ranking and preference learning, particularly in the context of large language models. The proposed framework is theoretically sound and provides a novel approach to addressing the limitations of existing ranking methods. The empirical results are compelling, demonstrating the importance of considering estimation noise and context-dependent performance variation. However, the article also raises important questions about the generalizability and computational complexity of the proposed framework. Future research should aim to address these limitations and explore the broader implications of this work for AI development and deployment.

Recommendations

  • ✓ Further investigation into the generalizability of the proposed framework across different applications and domains.
  • ✓ Development of more efficient algorithms for constructing simultaneous confidence intervals, particularly for large-scale datasets.

Sources

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