Nationally, there are less than 10% of incarcerated people in private prisons. This number starts to vary widely from state to state though, with some states having more than 50% and some having 0%.
And people in prisons (private or public) count towards total population in counties, giving them more weight in elections, despite none of the prisoners having chosen to be there voluntarily nor having the right to vote. https://www.vera.org/news/how-mass-incarceration-shapes-our-...
Except immigrants choose where they want to live.
The prisoners are where they are because the party in power (usually Republican, borderline neo-Confederate) creates laws that lead to extensive incarceration (such as "three strikes") and is the one which decides where to build prisons, which results in biased elections in their favor. Which reeks of the pre-civil war rules that slaves count for political weight.