I suggest that a set of 'closed' badges be added. Bronze for first question closed, silver for 10 questions closed, and perhaps a gold...
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Badges are meant to encourage good behaviour. The only exception to this is the Tumbleweed badge which is a consolation prize.
The most common close reason is probably duplicate, having these badges would just discourage people from checking before posting.
"It doesn't matter if it's a duplicate, it's one more to my total, gold