Earlier quoted context omitted.
Probably not. Stuff like getting rid of parole preceded private prisons. Private prisons is a trailing phenomenon that appears to be more about serving the huge demand for prison beds created by retributive policies. Washington State, for example still has no private prisons. But it enacted one of the country's early "three strikes laws" back in the early 1990s. Private prison companies have been clamoring to get an…
It's also worth considering that private prisons, once established, create perverse incentives to intensify those same retributive policies. A vicious recursion.
I think the most you can say is that private prisons (and public prison guard unions, which is probably a much bigger force) are slowing the retreat from 1980s/1990s retributive policies.