I think one way of correcting that would be by transforming our voting system into a knowledge-based democracy: If you do very well on certain exams testing your history, logic, and civics, then your vote counts 2x, 3x, or maybe 5x more than before.
This way we reward knowledge. Those who have more of it have more of a voice in politics. Those who have less of it likewise have less of a voice: their opinions count for less! It may seem unfair, but this system acknowledges that some opinions are better than others. That's simply how it is. Furthermore, you can't run for office unless you score in the top percentage, maybe the top 10%. People like Perry and Bachmann couldn't run for president in my society!! They're smply not qualified. Or if they would like to qualify, they will have to work harder to understand basic truths of economics, logic, and history.