Citizens of two racial groups choose whether to engage in illegal activities, and police audit citizens. Citizens are heterogeneous according to legal earning opportunities, which are distributed differently across groups. We define fairness of policing as policing groups with the same intensity, and effectivenesss of interdiction as reducing the amount of crime. We show that sometimes, forcing the police to behave more fairly can increase effectiveness of interdiction, and give exact conditions under which this is so. These conditions are based on the distributions of legal earning opportunities in the two groups, and are expressed as contraints on the QQ plot of these distributions.

Legal earning opportunities are not observable for those citizens who become criminals. However, we give conditions under which the QQ plot of legal earning opportunities equals the QQ plot based on reported income distributions (which are observable). We also discuss whether our notion of fairness is meaningful when the cost of being searched reflects the shame of being singled out by the police.