Well, I've just done this out of curiosity, but since a user is not allowed to upvote/downvote his questions/answers, is there any specific reason behind allowing him to vote for close his own question?
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
Why not? If the user has realized that it is a dupe or off topic, helping to close it seems like a sensible thing. I've done this plenty of times, generally with dupes.
Good samaritan. Ok, comparing this with upvoting/downvoting his own questions/answers.
That is my take... There might be many other reasons.