A Bayesian Model of Cash Bail Decisions

The use of cash bail as a mechanism for detaining defendants pre-trial is an often-criticized system that many have argued violates the presumption of "innocent until proven guilty." Many studies have sought to understand both the long-term effects of cash bail's use and the disparate rate of cash bail assignments along demographic lines (race, gender, etc). However, such work is often susceptible to problems of infra-marginality -- that the data we observe can only describe average outcomes, and not the outcomes associated with the marginal decision. In this work, we address this problem by creating a hierarchical Bayesian model of cash bail assignments. Specifically, our approach models cash bail decisions as a probabilistic process whereby judges balance the relative costs of assigning cash bail with the cost of defendants potentially skipping court dates, and where these skip probabilities are estimated based upon features of the individual case. We then use Monte Carlo inference to sample the distribution over these costs for different magistrates and across different races. We fit this model to a data set we have collected of over 50,000 court cases in the Allegheny and Philadelphia counties in Pennsylvania. Our analysis of 50 separate judges shows that they are uniformly more likely to assign cash bail to black defendants than to white defendants, even given identical likelihood of skipping a court appearance. This analysis raises further questions about the equity of the practice of cash bail, irrespective of its underlying legal justification.