How to offer a bounty on a question with unsatisfactory answers?

Question

I am very interested in a straightforward definition of the concept "positive regression dependency on each one of a subset" (with straightforward example a plus) as described by Benjamini and Yekutieli. Harvey Motulsky seems to share my interest: The meaning of "positive dependency" as a condition to use the usual method for FDR control. There has even been a bounty placed and awarded on this question.

However, none of the answers actually clarifies this this concept in plain language (although one answer with a single upvote does simply quote from Benjamini and Hochberg). The most voted on answer—which won a bounty for the question—does not actually answer the question… a point made abundantly clear in the comments following the answer, and also by the answer's lack of acceptance by the OP.

I have a feeling this kind of situation may not be unique.

Is there a way I can offer a bounty to encourage a solid answer, without it simply being awarded to a much up-voted yet poor answer?

References

Benjamini, Y. and Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29(4):1165–1188.

Answer 1

The basics are as follows:

1. If you place the bounty you can award it as you see fit.

2. If nobody posts an acceptable answer and so you don't choose to award the bounty, typically the bounty simply lapses unawarded (the reputation already having been lost).

3. Under particular circumstances, an unawarded bounty may be - fully or partly - awarded automatically. Detailed information here: How does the bounty system work? (search for "What is automatic awarding"):

   If the asker placed the bounty and accepted an answer that was posted during the bounty period but doesn't award the bounty, that accepted answer is automatically awarded the [full] bounty.

   Failing that, half the bounty is awarded to the highest-scored answer out of those which were posted after the bounty was started, have a score of at least +2 and were not written by the bounty starter.

   If none of these conditions apply, the bounty is not awarded.

You can't stop the auto-award, unfortunately, so it's a risk that you take that the bounty may be automatically awarded to an answer that may have been interesting enough to be upvoted but doesn't fully answer the question in the desired fashion. About the best you can do is call for something like a canonical answer in the bounty, downvote posts that really don't do what you seek and encourage others to do likewise -- but you can't make people vote the way you want, so a new answer could still end up with +2 net upvotes and get half the bounty anyway.