I see too many posts with bounties being abandoned on our site. Bounties are an efficient attention-getter device which does well to attract answers to the post. If the post is abandoned, this seems unfair to the people who invested their time in answering it.
My idea is inspired by the fact that if a poster accepts someone else's answer he gets +2 rep (link), which encourages acceptation. I would suggest a similar bonus for awarding bounties.
As +2 rep is a paltry amount when compared with bounties that are usually in the range of 50-200. My idea is that for a bounty being awarded by its poster (not the community), to refund the bounty-poster with something like 20 percent of his bounty. This is a positive type of encouragement which hurts no one.
To motivate bounty posters to return and indicate why the proposed answers didn't work for them, perhaps this award should also apply if they post an answer of their own during the 7+1 days bounty period.
Please indicate your opinion of my suggestion or your ideas for improvement.
Edit : Conclusion
We today have 63,676 unanswered questions, almost all abandoned, and the above +2 rep rule is too little to be effective.
I thought that because bounties are much more substantial there would be a numerical argument to offer a more effective incentive, including channeling back some of the reputation, but I didn't manage to start any brainstorming about the subject.
It has been suggested that meta.SE is more suitable for such a discussion, but in view of the evidenced inertia I don't think I'll bother.
Thanks to every one who participated.