Predictive policing systems are increasingly used to determine how to allocate police across a city in order to best prevent crime. Observed crime data (arrest counts) are used to update the model, and the process is repeated. Such systems have been shown susceptible to runaway feedback loops, where police are repeatedly sent back to the same neighborhoods regardless of the true crime rate. In response, we develop a model of predictive policing that shows why this feedback loop occurs, show empirically that this model exhibits such problems, and demonstrate how to change the inputs to a predictive policing system (in a black-box manner) so the runaway feedback loop does not occur, allowing the true crime rate to be learned.