Algorithms are now regularly used to decide whether defendants awaiting trial are too dangerous to be released back into the community. In some cases, black defendants are substantially more likely than white defendants to be incorrectly classi ed as high risk. To mitigate such disparities, several techniques have recently been proposed to achieve algorithmic fairness. Here we reformulate algorithmic fairness as constrained optimization: the objective is to maximize public safety while satisfying formal fairness constraints designed to reduce racial disparities. We show that for several past de nitions of fairness, the optimal algorithms that result require detaining defendants above race-speci c risk thresholds. We further show that the optimal unconstrained algorithm requires applying a single, uniform threshold to all defendants. e unconstrained algorithm thus maximizes public safety while also satisfying one important understanding of equality: that all individuals are held to the same standard, irrespective of race. Because the optimal constrained and unconstrained algorithms generally di er, there is tension between improving public safety and satisfying prevailing notions of algorithmic fairness. By examining data from Broward County, Florida, we show that this trade-o can be large in practice. We focus on algorithms for pretrial release decisions, but the principles we discuss apply to other domains, and also to human decision makers carrying out structured decision rules. ACM Reference format:1 We consider racial disparities because they have been at the center of many recent debates in criminal justice, but the same logic applies across a range of possible a ributes, including gender. arXiv:1701.08230v4 [cs.CY]

This study considers the circumstances under which members of the Muslim American community voluntarily cooperate with police efforts to combat terrorism. Cooperation is defined to include both a general receptivity toward helping the police in antiterror work and the specific willingness to alert police to terror‐related risks in a community. We compare two perspectives on why people cooperate with law enforcement, both developed with reference to general policing, in the context of antiterror policing and specifically among members of the Muslim American community. The first is instrumental. It suggests that people cooperate because they see tangible benefits that outweigh any costs. The second perspective is normative. It posits that people respond to their belief that police are a legitimate authority. On this view we link legitimacy to the fairness and procedural justice of police behavior. Data from a study involving interviews with Muslim Americans in New York City between March and June 2009 strongly support the normative model by finding that the procedural justice of police activities is the primary factor shaping legitimacy and cooperation with the police.

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Why do people believe that violence is acceptable? In this paper we study people's normative beliefs about the acceptability of violence to achieve social control (as a substitute for the police, for self-protection and the resolution of disputes) and social change (through violent protests and acts to achieve political goals). Addressing attitudes towards violence among young men from various ethnic minority communities in London, we find that procedural justice is strongly correlated with police legitimacy, and that positive judgments about police legitimacy are associated with more negative views about the use of violence. We conclude with the idea that police legitimacy has an additional, hitherto unrecognized, empirical property-by constituting the belief that the police monopolise rightful force in society, legitimacy has a 'crowding out' effect on positive views of private violence.