Multiagent language model systems, such as collaborative reasoning and debate, produce multiple correlated candidate answers and confidence signals. However, these signals are usually calibrated only at the individual agent level, and provide no principled confidence estimate for the system's final answer. We formulate this as a confidence composition problem where combining confidence across agents and reasoning stages while preserving both selective utility and probabilistic reliability. We study confidence-aware routing and log-odds pooling protocols that select among candidate answers and output a system-level confidence. Across five benchmarks, 30 heterogeneous and homogeneous model pairs, and two confidence estimators, our gated-fusion methods improve AUARC and reduce Brier score over single agent, standard debate, and selective debate baselines, while retaining competitive weighted F1-score as a correctness metric. We further show that our log-odds fusion is overconfident due to correlated intermediate signals. We propose a shared dependence discount that substantially improves reliability while preserving predictions.
Foundation model agents increasingly operate in multi-agent deployments where a coordinator must decide which agent's response to trust. The standard approach weights agents by their self-reported confidence, but recent evidence shows that foundation model confidence is systematically miscalibrated and, on hard tasks, inversely correlated with accuracy. Design-time calibration methods (temperature scaling, Platt scaling, histogram binning) cannot address this problem because they fit a fixed correction to held-out data and degrade under distribution shift. We present MARGIN (Multi-Agent Runtime Grading via Incremental Normalisation), an online calibration method that learns per-agent, per-confidence-band calibration factors from the task stream itself, requiring no model access, no held-out data, and no retraining. MARGIN uses symmetric exponentially weighted moving averages with Bayesian shrinkage blending, and has three hyperparameters with robust defaults. Across 18 foundation models, 8 benchmarks, and over 44,000 observations, MARGIN achieves 3-6x lower calibration error than the best design-time baseline under distribution shift. In multi-agent selection, raw verbalized confidence fails to beat random at pairwise resolution (43-50%) on hard benchmarks. MARGIN corrects this completely, raising pairwise resolution to 70-89% and closing 37-78% of the Raw-to-Oracle pass@1 gap across the five code-generation benchmarks without any oracle knowledge of which model is strongest. Six formal propositions characterize convergence, tracking speed, and the optimality of symmetric updates for non-strategic agents, with all predictions illustrated empirically.
Multi-agent debate systems are typically evaluated only on whether the final answer is correct, overlooking the quality of the intermediate reasoning that debate is designed to produce. This paper studies the relationship between three signals in multi-agent debate: token-level log-probability distributions over reasoning tokens, LLM-as-judge rubric scores assigned to those tokens, and final task accuracy. We examine whether internal confidence signals predict externally evaluated reasoning quality, and whether either signal aligns with task correctness, across three domains: rubric-based scoring, mathematical reasoning, and factual question answering. Our framework pairs a two-agent debate architecture -- a Constructor and an Auditor -- with an LLM-as-judge that scores each agent's reasoning along instruction following, justification quality, and evidence grounding, together with a critical-failure flag. Experiments in the rubric-scoring domain reveal a consistent four-phase confidence trajectory and a substantial role asymmetry: confidence aligns with judged reasoning quality roughly twice as strongly for the Constructor as for the Auditor, and confidence-based detection of critical reasoning failures is markedly more reliable for the Constructor (AUROC 0.804) than for the Auditor (0.634). These findings motivate the broader cross-domain investigation proposed in this paper.
Evaluating reasoning quality in multi-agent LLM systems is challenging, especially for open-ended tasks without reference answers. We investigate whether intrinsic confidence signals, token-level log-probabilities from decoding, can predict reasoning quality as assessed by LLM-as-judge evaluation. Using a debate-based essay scoring framework, we compare confidence proxies against rubric-based judge scores across two ASAP essay sets. We find that early-token confidence, particularly within the first few generated tokens, is consistently the strongest predictor of reasoning quality, outperforming full-sequence statistics. Analysis of log-probability trajectories shows that the opening phase of generation is the most heterogeneous and therefore most informative. We also observe a systematic asymmetry between agent roles, with stronger alignment between confidence and quality for supportive reasoning than for adversarial critique. These results suggest that early decoding dynamics provide a lightweight and effective signal for estimating reasoning reliability in multi-agent LLM systems.