Problem: People vote on offices/issues they know nothing about, because once they get to the ballot box to vote on the important office/issues, they feel like they have an obligation to vote on everything.
First-step Solution: Find ways to educate voters that it is okay to admit they don't know what the right choice is.
Long-Term Solution: Find ways to help educate potential voters so they feel comfortable voting for more and more offices/issues.
What happens to the ballot of someone who states no I voted D or R on everything
There is no place for someone to state that. We are asking them to sign that they agree to keep an open mind and make educated choices. If they refuse to sign, they don't get to vote. If they sign and lie, nothing happens, because there isn't a practical way to enforce it. Fortunately, people will sometimes do the right thing and keep promises they make even if they don't have to.
What happens if a voter refuses to answer the question
There is no question. The ballot looks like this:
[box] No vote ("I haven't done enough research to make an educated choice)
[box] Obama
[box] Romney
and for propositions:
[box] No vote ("I haven't done enough research to make an educated choice)
[box] Yes
[box] No
What if they can read but know the name of the candidate
Assuming you meant "can't," then they look for the name of the candidate.
Couldn't the same thing be accomplished by putting up a poster that says you are not required to vote on every candidate or issue
That's an alternative option. I don't think it would be quite as effective, but it might be cheaper. Also, I'd rather see a poster that says "you should not vote on a candidate or issue if you don't have enough information to make an educated vote."