# State-dependent error correlations shape voting thresholds in committees of AI agents

arXiv: https://arxiv.org/abs/2607.23931 · HTML: https://mlsanity.com/paper/2607.23931/

## Key facts

- Cited by 2 papers in the map (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 21 of its 51 references that are in the map.
- First posted on arXiv 27 Jul 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, 21 of 21)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [MetaGPT: Meta Programming for A Multi-Agent Collaborative Framework](https://mlsanity.com/paper/2308.00352/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [Get Your Vitamin C! Robust Fact Verification with Contrastive Evidence](https://mlsanity.com/paper/2103.08541/) (2021)
- [More Agents Is All You Need](https://mlsanity.com/paper/2402.05120/) (2024)
- [Multi-Agent Risks from Advanced AI](https://mlsanity.com/paper/2502.14143/) (2025)
- [Towards a Science of Scaling Agent Systems](https://mlsanity.com/paper/2512.08296/) (2025)
- [Algorithmic Monoculture and Social Welfare](https://mlsanity.com/paper/2101.05853/) (2021)
- [Picking on the Same Person: Does Algorithmic Monoculture lead to Outcome Homogenization?](https://mlsanity.com/paper/2211.13972/) (2022)
- [Great Models Think Alike and this Undermines AI Oversight](https://mlsanity.com/paper/2502.04313/) (2025)
- [Correlated Errors in Large Language Models](https://mlsanity.com/paper/2506.07962/) (2025)
- [When is a crowd wise?](https://mlsanity.com/paper/1406.7563/) (2014)

## Built on by (most cited first, 2 of 2)

- [The Exceedance Design Effect: Effective Sample Size for Thresholds under Clustering](https://mlsanity.com/paper/2608.21262/) (2026)
- [RAIM: Robust Aggregation of Inexpensive Models for Hallucination Detection](https://mlsanity.com/paper/2609.39229/) (2026)

## Abstract (arXiv)

The aggregation benefit of a committee of artificial intelligence (AI) agents comes from complementary information across members. Classical voting guarantees assume independent errors. Language-model errors often co-occur on the same cases. We combine Sah-Stiglitz screening with error dependence that can differ between good and bad cases. In a homogeneous exchangeable Gaussian-copula model, shared errors create a positive asymptotic error floor for majority voting and can change the approval threshold that minimizes expected loss. We estimate a heterogeneous extension from 174,384 votes cast by 28 language models on four binary-screening benchmarks. Parameters estimated from odd-indexed items predicted committee loss on even-indexed items. For the sampled committee composition, the full-matrix dependence model increased identity-line R^2 from 0.840 under independence to 0.967. In a design-balanced analysis, cost-sensitive threshold selection under independence reduced scaled loss from 60.25 for majority to 52.50. Modeling dependence reduced it further to 50.77, an incremental improvement of 1.73 units (95% bootstrap CI, 0.68-2.33). The overall reduction from majority was 15.73% (95% bootstrap CI, 13.41-16.75%).