Bregman Consensus

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.

When multiple LLM agents solve the same problem, standard practice compresses each agent's reasoning into a majority vote or layered synthesis, treating agreement as the finish line. We show this is unnecessarily lossy: an LLM aggregator that reads complete reasoning traces recovers correct solutions even when agents unanimously agree, with beneficial corrections consistently outweighing harmful ones -- the \emph{aggregation paradox}. Majority voting has a ceiling that perturbation diversity does not raise (error correlations are identical); the aggregator's gain comes from trace-level complementarity, assembling correct intermediate steps from minority chains that voting discards. These findings motivate Self-Consistent Mixture of Agents which generates trace diversity through semantic-preserving input perturbations, safeguards the majority via anchored refinement with provable non-degradation guarantees, and always synthesizes -- never gates on consensus. A single model with perturbation-induced trace variation outperforms heterogeneous model pools across structured reasoning, PhD-level science, competition mathematics, and competitive programming. The unit of aggregation should be the reasoning trace, not the answer.

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.