Australia

If we make it a prerequisite to vote that ones need to be able to answer some extremely basic questions about the election they're voting in, all of those questions being given months ahead of time, along with all the answers, then (barring profound mental conditions) not qualifying to vote is a choice. If you're informed enough to know where the polling booth is, you're probably capable of passing that bar. Based on your reply, you'd pass with flying colours.

If someone is so apathetic that they don't know the absolute basic premise of a given election, what is the benefit of allowing them to vote in it?

Of course, and I didn't emphasise this enough, the system I'm proposing relies heavily on the ability for the election organisers, through tools such as the government and law, to empower every possible voter to understand the basic premise of the election. And in a sea of corporate-owned media (both traditional and online), this is easier said than done, but far from impossible.

I think everyone deserves to be given the tools they need to have real political power. That's demo-cracy.