It is a simple question. Why does the bounty on a question that has no answers expire? Shouldn't it remain till it is answered, so that people have an incentive to figure out an answer later, even if they don't get it in that 1 week.
Also, why can't many people place multiple bounties on the same question, so the most popular unanswered questions can have accumulated extremely high bounties. Whether or not there should be an upper limit to this (say, 2000) is another matter.
That way, votes would be a measure of popular support, while the total bounty amount would be a measure of the support from more elite users. Also, people will be willing to put greater bounties, if they are guaranteed that it won't be wasted.
People may argue that the question may receive incomplete answers or imperfect proofs, just to acquire the bounty, but moderators can be told to be extra strict when choosing to delete such answers. The users who put the bounty should be given an option to remove it after a fixed period (say, 1 month). Whether he can claim part of it back (say, half of it) is again, another matter for discussion.