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Re-evaluating Open-ended Evaluation of Large Language Models
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Proposes evaluating LLMs as a 3-player general-sum game (prompt, king model, rebel model) and rating them via clone-invariant equilibrium solutions (NE/CCE selected with a novel affinity entropy) instead of Elo.
Problem
Elo-based open-ended LLM evaluation (e.g., LMSYS Chatbot Arena) is sensitive to redundant prompts and models, so it can bias model development toward specializing in over-represented skills and can be manipulated by adding redundant prompts.
Approach
Model evaluation as an N-player general-sum game between prompt, king and rebel players; ratings are regrets at equilibria selected by a novel kernelized affinity entropy (generalised Tsallis entropy with a similarity kernel) so that the selected equilibrium and ratings are invariant to cloned actions.
Key results
- Under up to 500 redundant adversarial prompts, gemini-1.5-pro-api-0514 consistently ranks first under the NE and CCE ratings, while its Elo ranking suffers once 250 adversarial prompts are added.
- Simulated Elo-maximizing model development shows a consistent decline in skill entropy, whereas equilibrium ratings preserve skill diversity.
- The CCE ratings tie the top-3 models for first place, while the NE ratings fully differentiate them.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| maximize Elo ratings with fixed initial prompts | model development in the simulated skill setting · simulated model improvement path | model skill entropy | Hurt |
| select additional prompts by high separability under Elo | model and prompt development in the simulated skill setting · simulated additional-prompts improvement path | skill entropy | Hurt |
| maximize equilibrium ratings instead of Elo ratings | model development in the simulated skill setting · simulated model improvement path | model skill entropy | Helped |
| maximize equilibrium ratings instead of Elo ratings | prompt development in the simulated skill setting · simulated prompt improvement path | prompt skill diversity | Helped |
| add redundant adversarial prompts | Elo ratings · arena-hard-v0.1 | model ranking robustness | Hurt |
| use affinity-entropy equilibrium ratings instead of Elo ratings | model rankings · arena-hard-v0.1 with redundant adversarial prompts | model ranking robustness | Helped |
| replace affinity entropy with Shannon entropy for QRE tracing (ablation) | NE ratings · arena-hard-v0.1 with redundant adversarial prompts | model ranking robustness | Hurt |
| replace affinity entropy with Shannon entropy for CCE selection (ablation) | CCE ratings · arena-hard-v0.1 with redundant adversarial prompts | model ranking robustness | Hurt |
| add cloned prompt actions | Shannon-entropy NE selection · general-sum Chicken game | equilibrium selection robustness | Hurt |
| add cloned prompt actions | Shannon-entropy CCE ratings · general-sum game | action ratings | Mixed |
Surprising findings
- Using Shannon entropy for equilibrium selection (max-entropy NE/CCE) fails to give clone-invariant ratings; in a Chicken game duplicating an action turns the max-entropy NE into the min-entropy NE.
- Redundant prompts receive identical ratings but notably lower equilibrium support, and highly rated prompts are played more often at equilibrium.
Limitations
- Results depend on a single judge (gemini-1.5-pro-api-0514) and may suffer from self-preference bias, so they are not an objective assessment of frontier LLMs.
- Invariance guarantee is lost for near-redundant prompts, though ratings degrade gracefully.
- Scaling further to larger prompt/model sets is challenging, and tabulating pairwise preference payoffs is costly.
Experimental setup
Datasets: arena-hard-v0.1
Benchmarks: arena-hard-v0.1
Metrics: Elo rating equilibrium rating (regret) ranking invariance under redundant adversarial prompts skill entropy
Baselines: Elo max-entropy Nash equilibrium (Shannon entropy) max-entropy CCE (Shannon entropy) arena-hard-v0.1 separability criterion
Builds on: Elo rating logit quantal response equilibrium linear tracing procedure Tsallis entropy arena-hard
Closest papers by meaning
- Elo Uncovered: Robustness and Best Practices in Language Model Evaluation (NeurIPS 2024 · similarity 0.91)
- Polyrating: A Cost-Effective and Bias-Aware Rating System for LLM Evaluation (ICLR 2025 · similarity 0.89)
- am-ELO: A Stable Framework for Arena-based LLM Evaluation (ICML 2025 · similarity 0.89)
- Accelerating Unbiased LLM Evaluation via Synthetic Feedback (ICML 2025 · similarity 0.89)
- LLMEval: A Preliminary Study on How to Evaluate Large Language Models (AAAI 2024 · similarity 0.88)
- PiCO: Peer Review in LLMs based on Consistency Optimization (ICLR 2025 · similarity 0.88)
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