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

• URL: http://arxiv.org/abs/2607.23931v1
• Date: Mon, 27 Jul 2026 02:06:22 GMT
• Title: State-dependent error correlations shape voting thresholds in committees of AI agents
• Abstract summary: We combine Sah-Stiglitz bootstrap screening with error dependence that can differ between good and bad cases.<n>We estimate a heterogeneous extension from 174,384 votes cast by 28 language models on four binary-screening benchmarks.<n>In a design-balanced analysis, cost-sensitive threshold selection under independence reduced scaled loss from 60.25 for majority to 52.50.
• Score: 1.7545090618311434
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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%).

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