How Much Does Correctness Cost? Budgeted Placement of Strong Correctors in a Weak Multi-Agent Swarm

A single human must audit $N$ LLM agents under a budget of $B \ll N$ audits per round, guided by self-reported confidence that may be adversarially miscalibrated and by correlated errors. We model this as budgeted noisy inspection over a two-level Gaussian copula and locate the miscalibration threshold $δ^*$ past which confidence-ranked auditing is \emph{worse} than random. Two a-priori expectations reverse: $δ^*$ \emph{rises} as the budget shrinks, and cross-family correlation is not low---shared difficulty dominates lineage. Five open-weight LLMs show operationally useless (near-constant) confidence, point estimates at or beyond the flip though CIs straddle it; a proprietary model is informative and lands below it. We give a quantitative criterion for \emph{vacuous} oversight, and replaying policies on recorded traces confirms the ordering.

Distributed agents in real-world settings frequently must coordinate under uncertainty with only partial observations. Coordination is necessary to share beliefs to aid in task completion, but communication costs bandwidth, introduces latency, and if done poorly, can degrade collective reasoning. This tension is especially acute in bandwidth-constrained deployments such as distributed sensing networks, autonomous reconnaissance, and collaborative cyber defense, where excessive transmission carries direct operational costs. Existing work has focused on multi-agent exploration and communication strategies, but not on how communication frequency and content jointly shape the collective belief state. Central to this challenge is the degree to which agents maintain compatible internal beliefs about the environment, a property we term \textit{epistemic alignment}. When agents share beliefs effectively, they converge on correct hypotheses; when communication is poorly designed, agents may converge confidently on wrong ones. We formalize this distinction and show it is not detectable from coordination metrics alone such as Jensen-Shannon Divergence or rate to consensus.

Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing