Equity in the Police Districting Problem: Balancing Territorial and Racial Fairness in Patrolling Operations

The Police Districting Problem concerns the definition of patrol districts that distribute police resources in a territory in such a way that high-risk areas receive more patrolling time than low-risk areas, according to a principle of territorial fairness. This results in patrolling configurations that are efficient and effective at controlling crime but that, at the same time, might exacerbate racial disparity in police stops and arrests. In this paper, an Equitable Police Districting Problem that combines crime-reduction effectiveness with racial fairness is proposed. The capability of this model in designing patrolling configurations that find a balance between territorial and racial fairness is assessed. Also, the trade-off between these two criteria is analyzed. The Equitable Police Districting Problem is defined as a mixed-integer program. The objective function is formulated using Compromise Programming and Goal Programming. The model is validated on a real-world case study on the Central District of Madrid, Spain, and its solutions are compared to standard patrolling configurations currently used by the police. A trade-off between racial fairness and crime control is detected. However, the experiments show that including the proposed racial criterion in the optimization of patrol districts greatly improves racial fairness with limited detriment to the policing effectiveness. Also, the model produces solutions that dominate the patrolling configurations currently in use by the police. The results show that the model successfully provides a quantitative evaluation of the trade-off between the criteria and is capable of defining patrolling configurations that are efficient in terms of both racial and territorial fairness.