Measuring Consensus in AI Agent Networks

Large language models are increasingly deployed as cooperating agents, yet their behavior in adversarial consensus settings has not been systematically studied. We evaluate LLM-based agents on a Byzantine consensus game over scalar values using a synchronous all-to-all simulation. We test consensus in a no-stake setting where agents have no preferences over the final value, so evaluation focuses on agreement rather than value optimality. Across hundreds of simulations spanning model sizes, group sizes, and Byzantine fractions, we find that valid agreement is not reliable even in benign settings and degrades as group size grows. Introducing a small number of Byzantine agents further reduces success. Failures are dominated by loss of liveness, such as timeouts and stalled convergence, rather than subtle value corruption. Overall, the results suggest that reliable agreement is not yet a dependable emergent capability of current LLM-agent groups even in no-stake settings, raising caution for deployments that rely on robust coordination.

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.

Multi-agent LLM systems can improve reasoning by pooling diverse perspectives, but their effectiveness depends on coordinating communication, particularly in hidden-profile settings where each agent holds only part of the evidence required for a correct decision. Existing protocols, including fixed schedules, round-robin exchange, and unstructured debate, provide no guarantee that a conversational action is appropriate. We propose Consilience, an inference-time orchestration framework that both steers and certifies multi-agent communication under distributed private information. At each turn, Consilience summarizes the discussion using a compact state capturing uncertainty, disagreement, evidence gain, redundancy, and premature consensus, then selects both a communication intervention (challenge, clarify, seek evidence, or route) and an appropriate speaker. Its central contribution is a round-wise conformal calibration procedure that provides a distribution-free, finite-sample guarantee: at each discussion round, conditional on reaching that round, the one-step regret of a controller's proposed action is bounded by a calibrated threshold with marginal probability at least 1 - alpha; an acceptance mechanism enforces the same guarantee for the executed action by replacing inadmissible proposals. On HiddenBench-style hidden-profile tasks spanning 12 open and closed weight language models, Consilience improves decision accuracy and communication efficiency over fixed and unstructured discussion protocols, sometimes surpassing a full-information baseline where every agent observes all evidence. These results demonstrate that certified adaptive communication control can be more valuable than increasing information availability, providing a practical mechanism for reliable multi-agent LLM coordination.