I think we should have a badge ( or a set of badges) for the users who close a sufficient number of questions. Closing question is a form of community service and therefore deserves rewards.
Note: Now don't try to close this question in the name of illustrating the irony :)!
This could make sense since closing is now a community process, requiring 5 votes to accomplish. That means that rather than awarding a badge based on simply voting to close (could encourage voting to close for no good reason), or based on casting the final vote (unfair to others who voted to close, and creates unusual incentives when votes approach 4 or 5), I'd propose that the badge be based on:
Casting X votes to close on questions which were then subsequently closed.
As an arbitrary suggestion, I'd say X = 25.
This means that everyone who votes to close would get credit towards their X, but only if the question was actually later closed (signifying that your vote was a "correct" vote). This does make it a little more attractive for those who wait until the 5th vote, but I don't see that as a major problem, as all voters still get credit.
I'd propose that questions that are re-opened should not rescind the associated tally, because a question could be re-opened after editing and be different from the form that was closed. Indeed, the close process can play a part in encouraging questioners to shape up their questions, and so the votes to close should still be recognized as a valuable part of that process even if it gets re-opened later.
The only problem I can see is that this kind of badge might be difficult to calculate and implement for the dev team, as it relies on keeping a tally on information which is transient in the system. It may not be technically feasible without major work.
To be honest, I'm not sure sure is such a good idea if the badge is awarded for closing a large number of questions as it might encourage some users to vote to close questions that may not need to be closed just to get the badge.
That said though, I think it would also be in keeping with the trend in some of the other badges to award one for the first question that you vote to close that is also closed as that would encourage users who just got their "Vote to Close" permissions to try them out which is how some of the other badges are designed.
I favor a 3 tier badge system with bronze, silver, and gold badges. It is not enough to close enough questions to get one badge, people should continually close questions that are duplicated content or require work from the asker to be up to standard.
All the rewards right now are stacked towards asking questions and answering them. We need additional gamification to encourage users to also keep this site clean. Closing questions is one of those mechanisms. Too few people do it.
I guess the real issue would be to determine how to issue - back in the olden days, any user with sufficiently-high rep could close. Now it takes a group effort.
And what about if the question is reopened? Does the 'Close' badge go away?
