Here is the concise version. The well-known Dunning-Kruger effect says that the less competent people are, the less they are able to recognize competence. Someone named Mato Nagel used this as the basis of a toy computer model of democracy. The result of his simulations is that the leaders selected by democracy are only slightly above average.
Of course there has been no testing of how accurate this model is. It is just a toy, and appropriate skepticism should be shown.
However I wouldn't say that evidence is against particularly against his conclusion. For instance 3 of the 4 remaining Republican candidates for President actively disbelieve the scientific consensus on topics such as evolution and global warming. (The exception is Mitt Romney, and even he is not convinced enough about global warming to say that we should spend any money on the issue.) Conversely surveys of Democrats find that most fail to accept basic economic theory on a number of subjects. For instance economists broadly agree that rent control decreases the supply of rental housing, but in surveys the majority of Democrats think that this is wrong.
I could start a debate by multiplying examples of widespread misconception on both sides, but these two are enough to support my point. My point is that it is easy to demonstrate that someone who actually understands and supports the best view of the world that experts from different fields have come to would be totally unelectable. That person might run the country very well, but will never, ever be selected by a democratic process.