It is not the privatization ...
It is the fact that the tax payers are paying X for every occupied bed, no ifs ands or buts.
Maybe the prisons should get paid X for violent crimes and Y for non violent crimes as an example.
And have the figures for X and Y be decided by referendum.
And to be honest, the definition of a crime should be revisited again. We have gone way over board. As an example I think a crime should be defined as follows:
A violation of property rights and the perpetrator is not able to satisfy the remedy imposed by a jury of his peers.
All judicial matters must be decided on a civil level and when, and only when, the perpetrator can not satisfy the remedy imposed by a jury of his/her peers, the case should be referred to the criminal courts.
There are so many checks and balances in a system like this, one could privatize the entire prison system and not encounter any abuses.