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Actually, democracy is based on the assmuption that one million and one men are wiser than one million men, so you are back to that one man again.
Look up Condorcet's jury theorem. Suppose a man has a 55% of making the right verdict. Now suppose that all members of a jury of five has the same chance. What is the chance that a majority in the jury reaches the right verdict?
What happens if you increase the size of the jury to twelve members?
You don't need much faith in people to appreciate the wisdom of democracy.
I'd say that democracy is based on the idea that it is better to let citizens vote their interests directly rather than have a smaller group decide for them. In the US, we only do that for the occasional proposition or referendum. In all other cases, democracy is heavily filtered through the political parties, the electoral college, etc., leading to a small group of leaders.