A common argument is that, because only a small fraction of US prisons are private [1], it means private prison lobbying is a negligible problem. But this is a fallacy! The fraction doesn't matter, only the absolute amount of funds flowing through private prisons, that are available for lobbying. That, and the political connections of prison owners that make lobbying more effective.
[1] Twenty-six states and the federal government incarcerated 99,754 people in private prisons in 2020, representing 8% of the total state and federal prison population. - https://www.sentencingproject.org/publications/private-priso...