I've seen that my question as been flagged "eligible for bounty".
What "mechanism" (if any) select between the questions the eligible ones ?
New questions are initially not eligible for having a bounty placed on them (I believe there are good reasons for this - mostly to do with potential abuse of the close system if there were no eligibility delay). Two days after the question has been posted, it becomes eligible for a bounty. Anyone with high enough reputation (75) can offer a bounty on an eligible question.