Another important aspect: if the public isn't sufficiently intelligent, or isn't interested in such things, how did that state come about? Does the government play any role in setting educational curriculum? Does the media play in any role in what the public focuses on, considers important, etc?
A large minority of them are, yes. There's millions of people in this country that flunked their way through 12 years of math class and never retained anything more than basic arithmetic. 4% of Americans are classified as "functionally illiterate", that's 13 million people who effectively can't even read.
The point of democracy is to placate everybody, not just the smarter portion of society, so the mechanisms of democracy should be simple enough for somebody with a simple mind to understand. "Count votes and pick who got the most" is generally such a system.