I've noticed that some questions are closed by a single vote. What's needed to give an user such a privilege?
A non-moderator user can cast a binding duplicate vote if they have a gold-badge in a tag originally on the question (and the usual criteria for dupe-closure are met). Note that these users are marked on these occassions with the symbol for a gold badge, a yellow circle.
To get a golden tag-badge one must have a total score of 1000 in at least 200 non-community wiki answers with this badge; the score is the number of upvotes (minus down-votes) a post gets. To track one progress one can look at the list of tags on ones user-page.
See posts tagged dupehammer for earlier discussion.