Recidivism prediction instruments provide decision makers with an assessment of the likelihood that a criminal defendant will reoffend at a future point in time. While such instruments are gaining increasing popularity across the country, their use is attracting tremendous controversy. Much of the controversy concerns potential discriminatory bias in the risk assessments that are produced. This work discusses a predictive bias criterion originating in the field of educational and psychological testing that has recently been applied to assess the fairness of recidivism prediction instruments. We show that, when recidivism prevalence differs across groups, the constraints imposed by the predictive bias criterion force false negative and false positive rates to also differ. We then demonstrate how differences in error rates can lead to disparate impact under policies that assign stricter penalties to higher-risk individuals.