The US puts a larger percentage of its population behind bars than any other country.
Commonly acknowledged, but wrongly. Look at the inflection points in the U.S. incarceration rate: https://upload.wikimedia.org/wikipedia/commons/4/48/U.S._inc...
Growth started in 1972-73. The growth rate kneed around 2000. Compare with the prison prison population: http://static.prisonpolicy.org/prisonindex/graphs/privatepri.... They were pretty much insignificant until the 1990's. By then, the growth trend in incarceration rates was firmly established, and indeed, was closer to the knee in 2000 than to the initial upswing in the 1970's.
What happened in the 1980's and 1990's? Privatization of many other government services: http://www.kevingunn.org/wp-content/uploads/2012/08/TotalFed....
The most reasonable conclusion from the data is that private prisons are not creating the demand for prisoners, but rather reacting to the demand for privatizing government services generally. I fully agree that private prisons should be illegal, but they didn't create the problem.
We created the problem, with three strikes laws and cracking down on probation. E.g. http://www.dc.state.fl.us/secretary/press/2001/timeserved.ht.... In 1991, Florida prisoners served about 35% of their sentences. Due to a state law, by 2001 it was 83%.