Good question, you should ask Quinton Tarintino, George Eastman, Peter Jackson, Richard Pryor, Peter Jennings and George Bernard Shaw. They never graduated High School. A diploma doesn't equate to intellect. Abraham Lincoln didn't have a diploma, he essentially taught himself after a certain point. Growing up on a farm he needed to be home to work and couldn't attend school. Imagine denying him the right to vote because he didn't have a "diploma." There are countless examples, I'm sure.
This really does bring up some great points, but one of the main ones that has yet to be stated is that a fundamental value of democracy is that every adult citizen has the RIGHT to vote and with out that you are infringing on the fundamental core of democracy.