Ranking Large Language Models with Human Preferences: A Game-Theoretic and Bayesian Comparative Study
Bibliographic record
Abstract
The rapid growth of large language models (LLMs) has created a demand for reliable, interpretable, and scalable ranking systems capable of comparing models based on human preferences. Traditional benchmarks often fail to capture qualitative nuances in open-domain dialog, where subjective judgments play a central role. In this work, we conduct a comparative study of six prominent ranking algorithms Elo, Glicko, TrueSkill, Bradley-Terry, Markov Chain-based ranking, and a novel HawasRank algorithm applied to the Chatbot Arena dataset containing 244,978 pairwise human preference comparisons. HawasRank is a divergence-based, game-theoretic ranking method inspired by Bregman optimization frameworks, designed to improve convergence speed, transitivity preservation, and computational efficiency in human-in-the-loop LLM evaluations. In this study, we carefully compare these algorithms based on several important criteria, such as predictive accuracy, the occurrence of transitivity violations, sensitivity to hyperparameters, convergence behavior, and CPU resource consumption. The findings of our analysis reveal the trade-offs that exist between different ranking approaches and offer practical guidance for choosing appropriate algorithms, especially in large-scale and evolving LLM evaluation environments.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.045 | 0.142 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".