Deterring repeat offenders with escalating penalty schedules: a Bayesian approach

We model deterrence with costly punishment when criminals have different abilities. Abilities are unobserved by both criminals and the courts. Based on past successes, criminals update their priors on being high-ability criminals. Courts cannot observe a criminal's total past offenses. They do know that criminals with more convictions were undeterred by previous penalties. Thus, they must have had more successes resulting in higher posterior probabilities of being high-ability criminals. Those with fewer convictions include more with lower posterior probabilities of being high-ability. Since they know that they are relatively more likely to be caught, they are deterred with lower penalties.