# Logarithmic Scores, Power-Law Discoveries: Disentangling Measurement from Coverage in Agent-Based Evaluation

arXiv: https://arxiv.org/abs/2604.00477 · HTML: https://mlsanity.com/paper/2604.00477/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 16 of 16)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [Agent-as-a-Judge: Evaluate Agents with Agents](https://mlsanity.com/paper/2410.10934/) (2024)
- [Personality Traits in Large Language Models](https://mlsanity.com/paper/2307.00184/) (2023)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [Assessing Judging Bias in Large Reasoning Models: An Empirical Study](https://mlsanity.com/paper/2504.09946/) (2025)
- [IntellAgent: A Multi-Agent Framework for Evaluating Conversational AI Systems](https://mlsanity.com/paper/2501.11067/) (2025)
- [Can LLM "Self-report"?: Evaluating the Validity of Self-report Scales in Measuring Personality Design in LLM-based Chatbots](https://mlsanity.com/paper/2412.00207/) (2024)
- [When AIs Judge AIs: The Rise of Agent-as-a-Judge Evaluation for LLMs](https://mlsanity.com/paper/2508.02994/) (2025)
- [Agent-as-a-Judge](https://mlsanity.com/paper/2601.05111/) (2026)
- [UXAgent: A System for Simulating Usability Testing of Web Design with LLM Agents](https://mlsanity.com/paper/2504.09407/) (2025)
- [Evaluating Large Language Models as Expert Annotators](https://mlsanity.com/paper/2508.07827/) (2025)

## Abstract (arXiv)

LLM-based agent judges are an emerging approach to evaluating conversational AI, yet a fundamental uncertainty remains: can we trust their assessments, and if so, how many are needed? Through 960 sessions with two model pairs across 15 tasks, we show that persona-based agent judges produce evaluations indistinguishable from human raters in a Turing-style validation. We then identify a score-coverage dissociation: quality scores improve logarithmically with panel size, while unique issue discoveries follow a sublinear power law-both exhibit diminishing returns, but scores saturate roughly twice as fast as discoveries. We hypothesize this reflects a power law distribution of the finding space: critical issues are discovered first by small panels, while corner cases require progressively larger panels, analogous to species accumulation curves in ecology. The mechanism traces to ensemble diversity-Big Five personality conditioning makes agents probe different quality dimensions, with expert judges acting as adversarial probes that push discovery into the tail of the finding distribution. A controlled ablation confirms that structured persona conditioning, not simple prompting, is required to produce these scaling properties.