Is democracy really worse than random?

I don't think the matter has been well tested.

Democracy might be worse than random if the qualities needed to win elections are too different from those needed to do the work.

Democracy might be better than random because democracy means that the most obviously dysfunctional people don't get to hold office. This is consistent with what I believe is the best thing about democracy-- it limits the power of extremely bad leaders. This seems to be more important than keeping extremely good leaders around indefinitely.