The Synthetic Consensus Trap: Correlated AI Errors, Verification Overload, and the Mathematics of Institutional Epistemic Cascades

Abstract

Institutions are beginning to use multiple large language models, AI agents, automated reviewers, and human overseers as if agreement among them were independent corroboration. That assumption can fail. This paper develops the Synthetic Consensus Cascade (SCC) framework, a multidisciplinary mathematical model linking correlated AI errors, human verification overload, automation deference, and downstream decision coupling. A beta-binomial latent-error model gives an exact expression for the probability that a majority of AI agents is simultaneously wrong. The model yields a central result: when pairwise error correlation remains positive, increasing the number of agents does not drive majority-error probability to zero; instead, risk approaches a non-zero correlation-dependent floor. A second layer models limited human review capacity and derives a critical verification-load threshold beyond which escaped errors can become supercritical in a branching cascade. In an illustrative stress test with individual error probability p = 0.08, nine agents, and error correlation ρ = 0.25, the majority-wrong probability is 3.56%, compared with 0.031% under independence, a 113.6-fold difference. Under separate illustrative review parameters, the cascade threshold occurs at verification load u⁎ = 1.84; expected error events over ten downstream generations rise from about 219 per 10,000 initial decisions below capacity to 3,281 at u = 2 and more than 10,500 at u = 3. These are not empirical forecasts. They are structural stress tests showing how modest correlation, overloaded oversight, and tightly coupled workflows can interact nonlinearly. The paper proposes measurable controls: error-correlation audits, epistemic diversity requirements, verification-capacity reserves, provenance separation, and cascade circuit breakers. The central implication is unsettling but operational: more AI agreement can create an illusion of safety precisely when shared failure modes make the system least independently verified.