Limiting Court Behavior: A Case for High Minimum Sentences and Low Maximum Ones

We model a simple justice system in which a court is mandated by society to assess the guilt and the punishment of an accused. The court takes prison facilities as given and neglects its impact on the cost to society of implementing the sentence. Clearly, the court, in this world, will condemn more often than society and assign higher penalties. Under these circumstances, society at large would necessarily benefit from having maximum sentences. We show, however, as a series of perverse results, that (1) maximum penalties need to be lower than the highest socially desirable penalty; (2) society would also benefit from imposing high minimum sentences even though it is precisely the harshness of courts, which it is trying to curb.