Epistemic Filtering and Collective Hallucination: A Jury Theorem for Confidence-Calibrated Agents

Multi-agent LLM systems often treat agreement as evidence: when many agents in a panel give the same answer, that answer is assumed to be more reliable. We show that this assumption can fail after agents communicate. Communication can induce correlated failures and false consensus, so the same vote share may reflect reliable agreement in one topology but over-confidence in another. We propose CAGE-CAL, a counterfactual agent-graph calibration framework for multi-agent LLMs. For each query, CAGE-CAL compares an observed post-communication agent graph with a matched counterfactual no-communication graph, capturing both pairwise failure correlations and group-level dependencies. Rather than simply counting how many agents agree, CAGE-CAL estimates the counterfactual shift between observed and no-communication dependence, and calibrates confidence accordingly. Across five benchmarks, CAGE-CAL improves reliability discrimination with competitive ECE, and its calibrated confidence further improves topology selection over the best fixed-topology strategy.

When the same question is asked of multiple AI advisers, as in self-consistency and LLM-as-a-judge panels, Condorcet's jury theorem predicts that adding independent, competent advisers makes the majority more reliable. The theorem, however, has a latent dimension when viewed from the user's vantage: adding advisers also makes disagreement more visible. A binomial model reveals that this ``visible dissent'' becomes nearly inevitable as the number of advisers grows, and that reliability and disagreement approach certainty at rates that cross at an adviser accuracy of 4/5 (0.8); below it, visible dissent eventually becomes more likely than a correct majority. Even ideal panels of independent and competent advisers can be correct in aggregate but appear divided; such disagreement does not by itself indicate aggregation failure. The way advisers split also provides a common basis for predictive multiplicity, reconciliation load, and reliance miscalibration. These results separate aggregation from disclosure and turn the latter into testable questions about how disagreement should be presented and interpreted.

Full-consensus rates are often treated as indicators of collective cognition, yet depend on how participation and final states are operationalized. We replayed 100 held-out human Wason groups with matched large language model (LLM) agent groups, seeding one belief-anchored agent per participant's pre-discussion answer and scoring agents and people with the same code. Across human scoring definitions, estimates ranged from 24.0% to 57.0%; about one fifth of participants never posted, whereas agents almost always did. Agent groups remained more consensual in two post-unblinding sensitivity analyses: the submit-based comparison (n = 98) yielded gaps of 34.0 and 43.9 percentage points for chat and reasoning modes, and the participation-matched comparison (n = 45) yielded gaps of 34.1 and 44.4 points. These complementary routes reduced different measurement asymmetries yet converged within 0.5 percentage points. The gap persisted without early stopping and under a reparameterization removing the memorizable answer; reasoning-mode groups then agreed nearly unanimously, mostly on incorrect answers. Simulated consensus did not track collective accuracy, and belief-anchored agent groups were biased estimators of the human group-outcome distribution in this setting. These analyses provide a scoring-explicit basis for assessing simulated-group estimates of human deliberative outcomes.