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 $\rho_{HM} < \rho^*$, with $\rho^* \approx a$ in the symmetric near-chance regime); (2) minimax bounds showing gains scale as $\Theta(\sqrt{\Delta d})$ with metacognitive sensitivity difference; (3) an impossibility result proving no confidence-based aggregation rule achieves complementarity when $\rho_{HM} \geq \rho^*$; and (4) multi-class generalization $\rho^*_K \approx \rho^*/\sqrt{K-1}$. 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.