This research paper explores the limitations of human-AI collaboration in binary classification tasks. The authors prove a "No Free Lunch" theorem, demonstrating that reliably combining human and AI predictions to always outperform the worst individual predictor requires essentially always deferring to a single source. This finding highlights the need for additional structural assumptions, such as prediction independence or learned knowledge of the joint distribution, to guarantee successful collaboration and achieve complementarity. The paper examines existing collaboration methods and explains why they succeed or fail in light of the theorem. It concludes by discussing implications for practical human-AI systems and proposing future research directions.

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