Algorithms frequently assist, rather than replace, human decision-makers. However, the design and analysis of algorithms often focus on predicting outcomes and do not explicitly model their effect on human decisions. This discrepancy between the design and role of algorithmic assistants becomes of particular concern in light of empirical evidence that suggests that algorithmic assistants again and again fail to improve human decisions. In this article, we formalize the design of recommendation algorithms that assist human decision-makers without making restrictive ex-ante assumptions about how recommendations affect decisions. We formulate an algorithmic-design problem that leverages the potential-outcomes framework from causal inference to model the effect of recommendations on a human decision-maker's binary treatment choice. Within this model, we introduce a monotonicity assumption that leads to an intuitive classification of human responses to the algorithm. Under this monotonicity assumption, we can express the human's response to algorithmic recommendations in terms of their compliance with the algorithm and the decision they would take if the algorithm sends no recommendation. We showcase the utility of our framework using an online experiment that simulates a hiring task. We argue that our approach explains the relative performance of different recommendation algorithms in the experiment, and can help design solutions that realize human-AI complementarity.
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