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

2026-07-26

AI Summary

This study addresses the limitation of traditional majority voting in AI agent committees, which assumes error independence despite large language models often exhibiting correlated errors due to shared knowledge. To overcome this, the work introduces state-dependent error correlation into the voting mechanism for the first time, integrating the Sah–Stiglitz screening framework with a heterogeneous Gaussian copula model to capture distinct error dependence structures in “good” versus “bad” cases. Leveraging these insights, the method dynamically optimizes cost-sensitive decision thresholds. Trained on 174,384 voting instances and validated via odd–even cross-validation, the full correlation matrix model improves loss prediction R² from 0.840 to 0.967. Compared to conventional majority voting, the proposed approach reduces scaled loss by 15.73%, substantially outperforming optimizations based on the independence assumption.

Abstract

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%).

Problem

• error correlation
• voting threshold
• AI committee
• dependence modeling
• language model errors

Innovation

• error dependence
• committee voting
• language models
• cost-sensitive threshold
• Gaussian copula