  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.
