What is the relevant population of prisoners who could be in a profit system? I have seen that only a small single digit percentage of prisons are for profit. It would be great to estimate the scale of those so I understand if this is a base case or edge.
There's much more profit in incarceration in general than just running private prisons. The whole system, much like the industrial military complex, is geared towards spending tax money on expensive contracts. There are no private wars out there (yet), it doesn't make defense any less profitable.
