One thing I've noticed in my own behaviour is that I will still answer a question even after voting to close as exact duplicate. I do this because there is no actual "reward" to close-votes.
This whole "gamification" is explained by Jeff himself.
I feel a little responsible for "Gamification", since we're often cited as an example (even, much to my chagrin, on Wikipedia). I wanted to clear up exactly why we made those choices, and specifically that all the gaming elements are there in service of a higher purpose. I play the Stack Exchange game happily alongside everyone else, collecting reputation and badges and rank and upvotes, and I am proud to do so, because I believe it ultimately helps me become more knowledgeable and a better communicator while also improving the very fabric of the web for everyone. I hope you feel the same way.
Part of this is the incentive of a reward. Answering a question, even a duplicate, with a valid and complete answer will gain you reputation, and possibly badges (including the elusive Reversal badge).
Casting a close vote and downvoting the question, however, yields absolutely no reward in itself, other than maybe a badge or two if you do it enough. Maybe.
I would like to suggest that casting a close vote which goes on to be the reason for closure of the question earns the voter about 20-30 reputation as a successful moderator.
For example, a user asks an off-topic question. Users A, B, D and E vote as off-topic, while user C votes as not constructive. The question is closed as off-topic (due to majority of votes). With this suggestion in place, users A, B, D and E will gain 25 rep for performing moderation duties, whilc C gains nothing because the close-voted for a different reason.
Hopefully this would dissuade users from answering duplicate and off-topic questions. Maybe there could be a reputation penalty (half the rep gained is lost?) for answering a question that goes on to be closed.