When machine-learning algorithms are used in high-stakes decisions, we want to ensure that their deployment leads to fair and equitable outcomes. This concern has motivated a fast-growing literature that focuses on diagnosing and addressing disparities in machine predictions. However, many machine predictions are deployed to assist in decisions where a human decision-maker retains the ultimate decision authority. In this article, we therefore consider in a formal model and in a lab experiment how properties of machine predictions affect the resulting human decisions. In our formal model of statistical decision-making, we show that the inclusion of a biased human decision-maker can revert common relationships between the structure of the algorithm and the qualities of resulting decisions. Specifically, we document that excluding information about protected groups from the prediction may fail to reduce, and may even increase, ultimate disparities. In the lab experiment, we demonstrate how predictions informed by gender-specific information can reduce average gender disparities in decisions. While our concrete theoretical results rely on specific assumptions about the data, algorithm, and decision-maker, and the experiment focuses on a particular prediction task, our findings show more broadly that any study of critical properties of complex decision systems, such as the fairness of machine-assisted human decisions, should go beyond focusing on the underlying algorithmic predictions in isolation.
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