Here's a map from a New Yorker article showing that the South is particularly lacking social mobility.
In these low mobility areas, it isn’t just black residents who tend to get stuck. Whites, too, exhibit low levels of social mobility. In states like Georgia, Mississippi, and South Carolina, poor white children tend to grow up into poor white adults. Secondly, regardless of race, the level of income inequality itself seems to play an important role in determining levels of social mobility. In places where income is divided very unequally, and poorer groups get only a small slice of the pie, very few people manage to start at the bottom and end up at the top.But they still vote against their (economic) interests.
Update 8thday has some excellent remarks in the comments below, chastising me for a certain elitism. (Go read!) To which I plead guilty. But I still think it's irrational to vote consistently against one's own economic interests.