When a "duplicate" close vote or flag is cast, a box appears above the question visible to the question's owner. It prompts the author to either edit the question to clarify its non-duplicateness or accept the duplicity by pressing a "yes, that solved my problem" button.

If the user chooses that button, the Community user casts the final duplicate vote, thereby saving close vote reviewers the trouble of closing a question that the author knows is a duplicate.