When Can Human-AI Teams Outperform Individuals? Tight Bounds with Impossibility Guarantees

Human-AI teams fail to outperform their best member in 70% of studies, yet no theory specifies when complementarity is achievable. We derive tight bounds for the broad class of confidence-based aggregation rules by integrating signal detection theory with information-theoretic analysis, yielding four results: (1) a complementarity theorem (teams outperform individuals iff error correlation ρHM < ρ^*, with ρ^* ≈ a in the symmetric near-chance regime); (2) minimax bounds showing gains scale as Theta(√Delta d) with metacognitive sensitivity difference; (3) an impossibility result proving no confidence-based aggregation rule achieves complementarity when ρHM ≥ ρ^*; and (4) multi-class generalization ρ^*K ≈ ρ^*/√K-1. Predictions match observed team accuracy (R = 0.94 on ImageNet-16H, R = 0.91 on CIFAR-10H) and the multi-class threshold scaling holds on human data (R = 0.93, K = 16), with robustness under non-Gaussian distributions. The framework explains why complementarity is rare and provides actionable design formulas; results apply to aggregation, not to interactive deliberation that generates novel answers.