Rehabilitation is the theory associated with the Idealist temperament and is the most refined of all four. To execute it properly, you have to inflict the exact same amount of harm the offender inflicted on you and of the exact same kind.
You say, essentially: “You hurt me greatly. But you don’t seem to care too much. Let me make you feel exactly as you made me feel, and maybe then you’ll understand how evil your actions were.” You do this for the sake of the offender, to reform him, to make him a better person.
This requires interpersonal utility comparisons which is subtle and tricky.
Retribution is the Guardian punishment. It, too, requires proportionality, but it’s more flexible, needing only the same amount of harm but not the same kind of harm. The case of theft is easiest and where retributive punishment is most similar to rehabilitative. Smith stole $2,000 from Jones, so Smith should first offer restitution to Jones, i.e., give the money back, but then he should also be punished extra with a $2,000 fine to paid to the government. However, the fine could in this case be replaced with, say, 30 days in jail.
Retribution is “justice.” Punishment inflicted for this reason is what the criminal “deserves.” The harm to the victim is fully deflected and is 100% redirected back onto the criminal in the manner of Newton’s third law. The proper cosmic order of things is thereby restored.
Deterrence, devised by Rationals to contain Barely Humans, no longer requires proportionality. However, it can feature it. A law stipulates a punishment of X years in prison for stealing a car. It so happens that without the law, car thefts would double; in other words, the law deters 50% of the relevant crime. In that case, from our utilitarian point of view, the harm spared to the victims must be balanced by the harm to the criminals from the state. X’s disutility should then be less than or equal to the average unhappiness felt by a car owner from having his car stolen.
It need not feature it, however. If (1) a fine of $10 deters 90% of car thefts, yet (2) 5 years in prison deters 90.1% of car thefts, then the former punishment is much better, since the thieves remain members of society whose happiness the legislator is trying to maximize. The harm to them from (2) is enormous, yet the social benefits are negligible. The cause of the greatest pleasure for the greatest number is better served with (1).
Condemnation, visited by Artisans upon Monsters, does not even require a crime! It’s not even punishment for any specific crime but preemptive social self-defense based upon a judge’s belief that the offender is totally depraved and will surely commit further crimes in the future. (In this case it differs from normal individual self-defense in the present.)