Unfortunately I don't have a source, but as I understand it, there are three important factors for effective punishment (as a deterrent and to prevent recurrenc

Unfortunately I don't have a source, but as I understand it, there are three important factors for effective punishment (as a deterrent and to prevent recurrence). Namely, that punishment should be certain, immediate, and proportionate. The criminal justice/carceral system of the United States achieves none of these. It's much more effective to have small, immediate certain punishments than disproportionately large punishments in a small fraction of cases. One reason for this is that humans are not good at estimating expected values, and vastly underestimate low probabilities.