One of the immediate conclusions which might be drawn from this is that people who are "stupid" vote differently from others. The unfortunate thing about this conclusion is that people who do not have a higher level of education are not necessarily stupid, or unintelligent, to use a more precise term. There are many reasons why people have not attained a higher education which have nothing to do with intelligence.
Note that I am not claiming there is absolutely no correlation between intelligence level and education level, only that one is not a cause of the other. I only wish to point out that on an individual level it is not valid to suspect that just because a person is uneducated that they have less mental capacity and decision making capability.
Next, take into account that the fact that a person has a higher level of education does not necessarily mean that they are better thinkers or more agile in solving practical problems than a person with a lower level of education. In fact, it is commonly know that many highly educated people get their degrees by cramming for exams and then promptly forget a large amount of what they crammed into their minds after their final exams have been completed.
In one way it is only normal for people who have a higher education to favour government involvement in their lives, because if it weren't for government funding and subsidies a great many of the institutions where they were educated wouldn't even exist. Just as animals don't bite the hand that feeds them, educated people would tend to support the forces which made it possible for them to get the education they received. And, in addition to this, since most of the institutions are supported by government largesse all of the teachers would have a tendency to reinforce a kind feeling at the least toward their benefactors.
From this perspective then, it is quite understandable that bigger governments will tend to support more higher education and expand opportunities to make more people able to receive higher education because it will result in a larger number of voters who would continue to support their existence.