# A No Free Lunch Theorem for Human-AI Collaboration

arXiv: https://arxiv.org/abs/2411.15230 · HTML: https://mlsanity.com/paper/2411.15230/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 21 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [On Human Predictions with Explanations and Predictions of Machine Learning Models: A Case Study on Deception Detection](https://mlsanity.com/paper/1811.07901/) (2018)
- [Uncertainty as a Form of Transparency: Measuring, Communicating, and Using Uncertainty](https://mlsanity.com/paper/2011.07586/) (2020)
- [When combinations of humans and AI are useful: A systematic review and meta-analysis](https://mlsanity.com/paper/2405.06087/) (2024)
- [Improving Expert Predictions with Conformal Prediction](https://mlsanity.com/paper/2201.12006/) (2022)
- [Human-Algorithm Collaboration: Achieving Complementarity and Avoiding Unfairness](https://mlsanity.com/paper/2202.08821/) (2022)
- [Improving Human-AI Collaboration With Descriptions of AI Behavior](https://mlsanity.com/paper/2301.06937/) (2023)
- [Role of Human-AI Interaction in Selective Prediction](https://mlsanity.com/paper/2112.06751/) (2021)
- [Teaching Humans When To Defer to a Classifier via Exemplars](https://mlsanity.com/paper/2111.11297/) (2021)
- [Towards Human-AI Complementarity with Prediction Sets](https://mlsanity.com/paper/2405.17544/) (2024)

## Built on by (most cited first, 8 of 8)

- [AI Agents for Inventory Control: Human-LLM-OR Complementarity](https://mlsanity.com/paper/2602.12631/) (2026)
- [AI-Assisted Decision Making with Human Learning](https://mlsanity.com/paper/2502.13062/) (2025)
- [Collaborating with GenAI: Incentives and Replacements](https://mlsanity.com/paper/2508.20213/) (2025)
- [Model Agreement via Anchoring](https://mlsanity.com/paper/2602.23360/) (2026)
- [The safe harbor paradox: when combining human and AI skills creates or destroys value](https://mlsanity.com/paper/2509.14057/) (2025)
- [Tree-Based Formalization of Multi-Agent Complementarity in Human-AI Interactions](https://mlsanity.com/paper/2606.04779/) (2026)
- [Human-AI Teaming Through the Lens of Calibration](https://mlsanity.com/paper/2606.10906/) (2026)
- [Human Decision-Making with AI Assistance under Correlated Features](https://mlsanity.com/paper/2606.20628/) (2026)

## Abstract (arXiv)

The gold standard in human-AI collaboration is complementarity -- when combined performance exceeds both the human and algorithm alone. We investigate this challenge in binary classification settings where the goal is to maximize 0-1 accuracy. Given two or more agents who can make calibrated probabilistic predictions, we show a "No Free Lunch"-style result. Any deterministic collaboration strategy (a function mapping calibrated probabilities into binary classifications) that does not essentially always defer to the same agent will sometimes perform worse than the least accurate agent. In other words, complementarity cannot be achieved "for free." The result does suggest one model of collaboration with guarantees, where one agent identifies "obvious" errors of the other agent. We also use the result to understand the necessary conditions enabling the success of other collaboration techniques, providing guidance to human-AI collaboration.