As I read here it is not possible to award a bounty to yourself. (Which makes sense, since it would make relatively easy to game the system.)
Imagine the following hypothetical situation: I ask a question where I am asking for some examples of some interesting thing. (For example, applications of some mathematical theorem.) I post a few examples, which I am aware of and then wait hoping to see more interesting examples. When I receive no new answers, after some time I put a bounty on that question. As times goes by, bounty is about to expire and no new answers were given.
In a situations similar to this I would say that the person who started the bounty was not trying to game system (getting more exposure of a question without actually losing rep), but it was an honest attempt to get more interesting answers to a problem she/he is interested in.
Would it be reasonable if in such situations the system awarded bounty, when it expires, to the most upvoted answer? (Assuming no other answers were given, and the person who started bounty answered this before starting the bounty.)