Comment by nlitened
I think there's also a fourth "end" to prison punishment, but I don't know the proper name for it.
It's when you remove the dangerous person from a society for a while, so they can't commit crimes for that while. This is very important part of prison punishment with people with criminal tendencies, and this is why recidivists get longer prison sentences for each subsequent repetition of a similar crime.
Unfortunately we have to admit that some (small) percentage of criminals cannot be rehabilitated, so they must be isolated from society.
The technical term is incapacitation. (Other commenters in this thread are also referring to it as “removal”.)
For criminals that act alone, variations in the severity of the sentence doesn’t seem to have the impact you might expect it to have on how much it actually deters people. (And there is the issue that people in prison can share strategies between themselves for how to more effectively commit crime, which is not an ideal outcome.) So indeed, incapacitation is a very important factor. When it’s studied, you often see numbers like “increasing the sentence by 10 years prevents 0.2 crimes due to deterrence and 0.9 crimes due to incapacitation”.
I say this applies to people acting alone because, although I have no proof, I suspect that organized crime is a bit more “rational” in their response to changes in sentencing. If sentencing were set up so that engaging in a category of crime was not profitable for the criminal organization, I’m pretty sure they would realize this and stop. This logic doesn’t apply to individual people, because the average person committing a crime has no idea what the sentence is or their odds of getting caught, and they obviously don’t do it often enough that the random variation is amortized out.