When Individually Calibrated Models Become Collectively Miscalibrated

• URL: http://arxiv.org/abs/2605.18858v1
• Date: Thu, 14 May 2026 05:25:16 GMT
• Title: When Individually Calibrated Models Become Collectively Miscalibrated
• Abstract summary: We show that individually calibrated predictors can become collectively miscalibrated when their predictions interact strategically.<n>We prove that under Brier-score-based aggregation with positively correlated beliefs, each agent's individually optimal report systematically underestimates the positive-class probability.<n>In contrast, VCG-based aggregation aligns incentives by rewarding marginal contribution, achieving dominant-strategy incentive compatibility and near-optimal performance.
• Score: 3.556355987197792
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Probabilistic prediction systems often aggregate probability estimates from multiple models into a single decision. A common assumption is that if each model is individually calibrated, the aggregate prediction will also be well calibrated. We show that this assumption fails in multi-agent settings: individually calibrated predictors can become collectively miscalibrated when their predictions interact strategically, in the game-theoretic sense of Brier-optimal local response, even without deliberate coordination. This phenomenon arises naturally when agents are independently trained on overlapping data. We prove that under Brier-score-based aggregation with positively correlated beliefs, each agent's individually optimal report systematically underestimates the positive-class probability, yielding a Price of Anarchy greater than one whenever Cov(b_i, b_j) > 0. In a canonical setting (n = 5 agents, pairwise correlation = 0.5, base rate = 0.3), the empirically measured PoA in false-negative rate reaches 7.25x. In contrast, VCG-based aggregation aligns incentives by rewarding marginal contribution, achieving dominant-strategy incentive compatibility and near-optimal performance. Experiments on three real-world datasets (NSL-KDD, UNSW-NB15, Credit Card Fraud) show that VCG provides strong robustness while maintaining comparable accuracy. It performs particularly well in data-sparse and adversarial settings, and adaptive weighting further improves performance under distribution shift.

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