Co-Failure Ceiling Caps Routing, Voting, and Mixture-of-Agents Gains Across 67 Frontier Models

arXiv 2606.27288·high signal

A new study shows multi-model LLM systems (routing, voting, cascades, fusion, mixture-of-agents) can never exceed accuracy of 1 minus beta, where beta is the rate at which every model is wrong on the same query. Crucially, the field's usual diagnostic — average pairwise error correlation (rho) — cannot identify beta, so reported ensembles may chase gains that are mathematically unreachable. Tested across 67 frontier models, it gives builders a single number to measure before investing in any multi-model orchestration layer.