Privatizing the social correction sector is a joke of really bad taste. Incentives are exactly like that, to increase recidivism and not actually re-socialize inmates.
You'd think that competition would foster better correction facilities, but as with big pharma, being effective is counterproductive because it hinders growth, which is at the core of capitalism.
Not saying competition is bad, only that it's maybe not universally applicable to all areas.
Inmates are products, not consumers. Consumers would be governments, and they would in theory over time select those administration companies that would offer the best correction facilities for the lowest price.
However, I am actually making the point against that. Privatization of that area makes no sense at all. I might have phrased that in a way that works against the central point of my argument, but the idea is that no, there is no competition that could possibly justify privatizing the corrections sector.
If the competition were set up with the right incentives, like payment to the private prisons based on their recidivism rates or job placement after incarceration, it might actually work. But today we're creating backwards incentives.
Failure to consider holistic societal gains is not something new for Americans at least. Both for tax payers and corporations, making any inmate a productive tax payer would be better for society and for shareholder value.