To increase p'-p, prisons need to incarcerate prisoners which are less prone to recidivism than predicted. Given that past criminality is an excellent predictor of future criminality, this leads to a perverse incentive towards incarcerating those who were unfairly convicted (wrongly convicted innocents or over-convinced lesser offenders).

If past criminality is a predictor of future criminality, then it should be included in the state's predictive model of recidivism, which would fix the predictions. The actual perverse incentive here is for the prisons to reverse-engineer the predicted model, figure out where it's consistently wrong, and then lobby to incarcerate (relatively) more of those people. Given that (a) data science is not the core competency of prison operators; (b) prisons will make it obvious when they find vulnerabilities in the model; and (c) the model can be re-trained faster than the prison lobbying cycle, it doesn't seem like this perverse incentive is actually that bad.