If punishment is an act designed to reprimand a criminal for his criminal actions, the use of force is a legitimate tool to enforce it.
The question I have however is how would punishments be enforced in a libertarian society?
I have recently read a Rothbard article where he theorized that in a libertarian society, there would be much less prisons. Instead, a judge would force a criminal to financially pay his of her victim(s) back. If something like a Ponzi scheme were to happen and the criminal didn’t have enough to pay back all his victims, Rothbard says that he could work for a victim as an indentured servant (even though I don’t see how you can be the indentured servant of many victims).
The issue toughens in the case of murder, or rape. If a murderer is convicted, I don’t see a lot of people accepting a murderer as a personal slave. Personally, I would be scared to have someone wh has killed my wife within my house.
One solution I found was a private prison system. A private judicial company could either provide prisons for free, or you may have to pay a certain fee based on the desired stay of the prisoner. I believe this is workable. But then, why are there so many libertarians simply opposing prisons, calling them creatures of the State?