Here is a simple model. Assume you need a certain intelligence to understand a crucial, policy-affecting idea (we can make this a fuzzy border and talk about this in distribution to make it more realistic later). If you are below this level your policy choices will depend on taking up plausible-sounding arguments from others, but it will be uncorrelated to the truth. Left alone such a population will describe some form of random walk with amplification, ending up with a random decision. If you are above the critical level your views will be somewhat correlated with the truth. Since you are affecting others when you engage in political discourse, whether over the breakfast table or on TV, you will have an impact on other people, increasing their chance of agreeing with you. This biases the random walk of public opinion slightly in favour of truth.

From most models of political agreement formation I have seen, even a pretty small minority that get biased in a certain direction can sway a large group that just picks views based on neighbours. This would suggest that increasing the set of people smart enough to get the truth would substantially increase the likelihood of a correct group decision.