It would be cool to do research like this paper from Maria Petrova.
The author does, however, assume that better informed voters will vote for better policy – “independent media is important for the quality of governance.” Thinking of Caplan’s book, I was skeptical at first but realized that his argument seeks to explain why the collective decisions of the electorate are as bad as they are given some level of information (is this right, John?). A better informed electorate might vote relatively well, though still poorly by economists’ standards. Of course, for many poorer countries, “relatively well” means a huge step up.
It might also be possible for the quality of voting to decline as the public becomes more aware of what their representatives are doing, depending on your point of view. For example, Petrova mentions in her paper that “countries with low media freedom. . .have lower level[s] of social spending (Petrova 2007).” As elected officials become more responsive to the public, Caplan’s preferences over beliefs become more of a problem. So, increasing the amount of independent information (where non-independent information is assumed to be discounted by voters and thus doesn’t create incentives for politicians) available to voters has mixed effects. Voters usually dislike corruption but applaud trade barriers. This ties in with that article about the success of China’s authoritarian government. Looking at the world today, though, it looks like countries with freer media and hence more information tend to perform well more consistently than ones where information is more limited. MR had a post about growth in democracies vs. non-democracies a while back.