Unless by Postgraduate Study that you mean "Educated" I really don't see how this is the case.
WC, people 'with a college degree' are not very educated in America, as far as I have noticed. So, yeah, I'd say 'educated' means post graduate - at least a master's degree.
I think that's a good point. We need to define "educated." Back in the day, a person with a degree in something like "business" (if that existed), would not be considered educated at all. They would be considered an uncultured tradesman. Indeed, elites used to disdain those who sullied their hands toiling at a "trade." "Educated" meant that you were cultured, lettered, could read latin and were basically what modern Americans would call, "a pretentious, nerdy homo."
By that old-time definition of educated, I think generally more educated = more liberal.