MARGIN: Runtime Confidence Calibration for Multi-Agent Foundation Model Coordination

Abstract

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.