The general claim is that Kennedy won by voter fraud in Illinois and Texas, and if both Illinois (27 votes) and Texas (24 votes) had gone to Niixon, it would have been 270 for Nixon, 252 for Kennedy, and Nixon would have won. I think the “Illinois voter fraud” is focused on because the alleged fraud was so egregious.
And a previous one: http://boards.straightdope.com/sdmb/showthread.php?t=275499
Seems people are very against such a system.
Only if I get to determine what’s on the test. I will grade it according to how well people agree with my opinions. Because, if they don’t agree with me, then clearly they don’t actually “understand what the voting is about”, now do they? 
I kid, but not by much. There are lots of subtle ways to bias a test like that.
Isn’t that a bit of a false dichotomy, though? I mean, not that I’m in any way endorsing the OP’s plan, but what if your choices are a simple-minded old man from Harlem who lived his life in the service of his family, friends and neighbors, and a genius Harvard professor who spent his entire professional life studying political science, sociology and/or economics, and who is a truly ethical, goodhearted, decent human being who loves his family, gives back to his community, and has devoted his life to figuring out how to improve society?
I’m quite leery of the anti-intellectual tendencies which tell us that simple homsepun folk wisdom are the answers to all of life’s problems. What does the simple-minded man from Harlem think about NAFTA? Does he know whether Global Warming is real? How does he feel about ethanol subsidies and alternative fuel research? How much did he know about Al Qaeda before 9/11?
Well it seems in some states this is already the case!
CONSTITUTION OF THE STATE OF IOWA – CODIFIED
ARTICLE II.
RIGHT OF SUFFRAGE.
Disqualified persons. SEC. 5. No idiot, or insane person, or person convicted of any infamous crime, shall be entitled to the privilege of an elector.
Even if we did tie voting privileges to a particular level of education or intelligence, I don’t think it would make much of difference to the outcome.
The big problem I have with this idea is how would you decide who is and is not qualified to vote? Who makes that decision? It seems a bit naïve to think that it could ever be fairly executed.
I also have to agree with filemat, it is more an issue of knowledgeability with the issues than intelligence or education.
This is self-regulating anyway, isn’t it? I mean low IQ people would be more inclined to watch Wheel of Fortune and read the National Inquirer and therefore wouldn’t have a clue who to vote for in the first place. So, they don’t vote.
In Canada their has been some discussion on implementing mandatory voting, which I believe you have in Australia. I am totally against that for the above reason. I say letting the morons opt out of voting would be more beneficial.