As incentive for voting to close questions, I was thinking of a badge given to who voted to close X questions, which were then closes, and where the user was the first user to vote.

The badge could be an incentive to vote to close, but as the badge is given to the first users who votes to close, there should not be an increment of wrongly closed questions.

There could be a silver badge, and a gold badge.
I didn't think for how much closed questions the badge should be gained. To decide that, we should look at the number of questions a user normally vote to close, and how many of those questions are really closed, then.

If the definition of the badge is not too restrictive, then questions that are re-opened after Y days should not be considered.