Blorgbeard's suggestion is excellent. If the OP accepts an answer, then it makes sense that, in the absence of any other activity, the full bounty should be awarded to that answer. I would be against imposing any awards before the expiration time, though: perhaps the OP wants to maintain the bounty until the last minute, waiting for a better, more complete response.
Grace had two important points against this:
- answers could have been accepted previously to the bounty
- the bounty could have been placed by somebody else
The first case do not really apply here, since there is no acceptance action during the bounty. Thus, the default 50% award should be maintained in this particular case. That is, of course, unless the OP changed which answer is accepted during this time frame.
On the second case, the bounty placer can receive a notification stating that the bounty question has an accepted answer, and inviting the user to evaluate awarding the bounty, e.g., in this question, if YOU accepted an answer, then Pekka would be notified. Pekka may then award the bounty to the accepted answer, another answer, or not award it at all. If not, then the default procedure remains.
Yoda states that "Automatic bounty awards are always a bad idea". I do not agree with that sentence, mostly because it is very unfair for users that spend time researching an answer to not receive any reward if the OP does not show up in a week or just forgets about the bounty. Furthermore, I do not see how this new scheme would be any different in that respect: if not manually awarded, bounties now are awarded in an automatic way at the end of their period. Changing the awarding rules does not make the procedure more or less automatic. After reading all the comments, Yoda's meaning seems to be "automatic award to the accepted answer is a bad idea" instead. I believe his example is the only situation in which the 50% award rule is the intended outcome, and I see it as a very unlikely (or, at least, rare) situation, without sufficient merits to support this ruling system. I do not have a definite position really about the voting for the bounty. It could be fair, but it's quite a complicated scheme.
Last caveat: The logic path seems a little more convoluted this way, but it's nothing that a couple of if/then blocks in the script could not solve.