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The field of fair machine learning aims to ensure that decisions guided by algorithms are equitable. Over the last decade, several formal, mathematical definitions of fairness have gained prominence. Here we first assemble and categorize these definitions into two broad families: (1) those that constrain the effects of decisions on disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions typically result in strongly Pareto dominated decision policies. For example, in the case of college admissions, adhering to popular formal conceptions of fairness would simultaneously result in lower student-body diversity and a less academically prepared class, relative to what one could achieve by explicitly tailoring admissions policies to achieve desired outcomes. In this sense, requiring that these fairness definitions hold can, perversely, harm the very groups they were designed to protect. In contrast to axiomatic notions of fairness, we argue that the equitable design of algorithms requires grappling with their context-specific consequences, akin to the equitable design of policy. We conclude by listing several open challenges in fair machine learning and offering strategies to ensure algorithms are better aligned with policy goals. 

Field studies in many domains have found evidence of decision fatigue, a phenomenon describing how decision quality can be impaired by the act of making previous decisions. Debate remains, however, over posited psychological mechanisms underlying decision fatigue, and the size of effects in high-stakes settings. We examine an extensive set of pretrial arraignments in a large, urban court system to investigate how judicial release and bail decisions are influenced by the time an arraignment occurs. We find that release rates decline modestly in the hours before lunch and before dinner, and these declines persist after statistically adjusting for an extensive set of observed covariates. However, we find no evidence that arraignment time affects pretrial release rates in the remainder of each decision-making session. Moreover, we find that release rates remain unchanged after a meal break even though judges have the opportunity to replenish their mental and physical resources by resting and eating. In a complementary analysis, we find that the rate at which judges concur with prosecutorial bail requests does not appear to be influenced by either arraignment time or a meal break. Taken together, our results imply that to the extent that decision fatigue plays a role in pretrial release judgments, effects are small and inconsistent with previous explanations implicating psychological depletion processes. 

Recent work highlights the role of causality in designing equitable decision-making algorithms. It is not immediately clear, however, how existing causal conceptions of fairness relate to one another, or what the consequences are of using these definitions as design principles. Here, we first assemble and categorize popular causal definitions of algorithmic fairness into two broad families: (1) those that constrain the effects of decisions on counterfactual disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions almost always—in a measure theoretic sense—result in strongly Pareto dominated decision policies, meaning there is an alternative, unconstrained policy favored by every stakeholder with preferences drawn from a large, natural class. For example, in the case of college admissions decisions, policies constrained to satisfy causal fairness definitions would be disfavored by every stakeholder with neutral or positive preferences for both academic preparedness and diversity. Indeed, under a prominent definition of causal fairness, we prove the resulting policies require admitting all students with the same probability, regardless of academic qualifications or group membership. Our results highlight formal limitations and potential adverse consequences of common mathematical notions of causal fairness.