It's not clear to me that a private system of law would have any prisons, private or otherwise. At most, I'd expect very temporary jails for pre-trial, but the risk of having to pay restitution for kidnapping in the event that the suspect was found not guilty would make insurance very expensive. ;)
I agree. You'd still have to figure out what to do with violent sociopaths, repeatedly breaking laws and not showing any signs of change. I would probably agree to pay to keep em locked until (if ever) they are considered not dangerous to the society.
