This post is co-authored by Timur Behlul.
This follows from my post last night, which essentially states that virtuous behaviour is more or less the same as behaviour associated with not discounting the future: exercise, saving, temperance, and good manners. Conversely, acts of vice are associated with higher subjective discount rates.
If this line of thought is correct, then the following story should hold:
Two potential thieves consider robbing a store. They both have the same expectation of being caught, and the punishment for both potential thieves would be the same. If the two potential thieves differ only in their subjective discount rates, then there exists some level of punishment which will induce criminal behaviour in the potential thief with the higher discount rate, and will result in the thief who considers the future with more value not doing the crime.
Likewise, if the two thieves are able to be punished with different sentences, there exist two different sentences at which both thieves will not engage in the crime at the margin. The thief with the lower discount rate requires a shorter potential sentence as a deterrent than the other.
To the extent to which these two statements are true, there exists an argument that the deterrent sentences imposed on different criminals should be proportional to their subjective discount rates.
However, for a prospective criminal to be aware of the potential consequences of their actions, there must be complete knowledge over how their punishment is elastic to the court's perception over their subjective discount rate. This would require a publicly known set of proxies for discounting to be known.
So if people who smoked, saved little (relative to peers in their income bracket), had plenty of speeding fines and the like, were made aware their potential crime would result in a higher length of imprisonment than if they didn't smoke/did save/didn't speed, there would simultaneously exist incentives for people to review their potentially in-virtuous behaviour at both ends---crime and smoking.