When Do Humans and Machines Truly Complement Each Other? Formal Conditions and Empirical Evidence for Human-AI Synergy

Can humans and artificial intelligence cooperate such that their combination yields greater accuracy than either agent alone? This result, termed \emph{synergy} or \emph{complementarity}, is notoriously difficult to achieve, even when both agents possess significant independent accuracy. In this paper, we present a formal framework to model human-AI interaction through the lens of reliance patterns, which characterize the joint correctness structure of human and algorithmic decisions. We derive mathematically necessary and sufficient conditions for synergy, demonstrating that its emergence depends on the ability of either agent to identify and correct the errors of the other, what we call...

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