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This question was recently edited to add a cash bounty. We already had one of those in the past, but with a different flavor. Are cash bounties appropriate for MO?
Personally, I see no problem at all. Some mathematicians are since way before MO fond of adding some (often small to negligible) monetary or other award to their problems. Why should one forbid this on MO.
In fact I could only see one justification to forbid this, namely that somebody would explain that there might be some legal problems.
I'm not so sure. I suppose one could have concern that if one offers a bounty for a result, perhaps there will be the perception that the result was "bought". If one purchases a theorem from another mathematician, do the standard academic practices of citation still hold, or would you expect everyone to believe the result is the purchaser's?
So part of me leans against the idea of allowing bounties outside the already-existing MO system of bounties. But I don't have strong feelings on this.
Heck, I think MO should encourage cash bounties, especially for questions easier than the money problems of Erdos and Talagrand.
I am not so sure about allowing the prize of a live goose, though...
@Ryan: I do not think that, say, Erdos considered any solutions to one of his money problems as one of his results. Neither do I think that anybody will think that Clay will 'own' the proof of some of the 6 out of 7 problems if ever they should be solved and the solver will accept the money. Moreover, if I would want to do things in a grey-area of academic practices I might not do so worldreadable on MO.
Finally, if one can 'buy' a result with 100 Euro why not with 500 reps? (If the practice of assigning relevance to MO presence in admission procedures and alike catches on, these points could get some actual value after all; indeed, joking aside, I am much more worried about such developments, than that somebody will 'buy' results on MO and then not quote the 'producer'.)
quid: Offering cash bounties on MO is new ground -- importing the interpretation that it should mean roughly the same thing as if the Clay Institute offered a bounty, or Erdos or someone like that, well that's something we should be clear about. Meaning that MO isn't a place for offering arbitrary economic contracts, the standard practices from academic mathematics culture are assumed.
@Ryan: Agreed, it is best to be explict about this. Indeed, the current question references Erdos explictly.
And, of course, the question/offer needs to meet the MO criteria for a question just like any other question. (Though, if I understand correctly, point bountys protect from closure, I would say we should not adopt this [infomally] for money-bounties.)
I have no objection in principal to MO questions including a cash bounty, although I can't imagine offering one myself. I would object to the "buyer" claiming the result as their own, and would certainly voice my support to the "seller" who claims that they should receive the correct citation/attribution. Because of that concern, if there are to be cash bounties on mathematical questions, I strongly support them being offered and answered in a public forum like MO, so that there is a permanent public record of who provided the answer.
@Valerio: For your information, it's likely people would have answered your question without the cash bounty. The landscape of mathematical personalities that I know strongly suggests perhaps a cash bounty de-motivates some people.
I think I was the first to raise some concern about the offering, and Francois created this meta thread afterwards.
My concern is that people will created titles like "$X bounty: problem title", which to me puts emphasis on the bounty, not on the problem hinted at in the title. I think it is more in the spirit of the forum to say "Problem title (bounty offered)", which places more emphasis on the problem. Also, by placing the bounty amount somewhere in the post, and leave it out of the title, people are encouraged to read through some of the post, even by those who just want to know how much is offered for solving the problem.
I also think (bounty offered) can be changed to (bounty paid) or (bounty withdrawn), if bounty status becomes important. However, the bounty should not get more emphasis than the problem. Also, the MathOverflow system uses square brackets  for things like [closed], so if this format is adopted I will strongly suggest that parentheses () are used for bounty status.
Finally, it is my hope that bounties remain an occasional item, and that I don't start using MathOverflow as a way to make quick coffee or beer money.
Gerhard "...User Interfaces Would Be Unstable" Paseman, 2011.11.25
"beer money", Gerhard? Heck, for 100 euros you can still buy a decent bottle of wine.
Perhaps, but since I don't travel much, I might have to pay for shipping. Also, I'm going for (the fame and theory behind solving) the big bounty items offered by Erdos. Then maybe I can afford a plane ticket AND a latte and a pint of dark. Or they might be given to me. Who knows.
Gerhard "Don't Bother To Dream Small" Paseman, 2011.11.25
@Ryan: for your information, the question was around without a bounty for fairly long.
Of course, in view of the fact that Mathew Daws declined the bounty it is evident that he did not answer 'for the money'. And, there was added personal motivation with the last revison, too.
So in some sense I am not sure whether I agree or disagree with you.
I'd say whether the bounty was relevant at all is hard to tell; however what I think could have made a difference (except it was a purely random effect that the person having an answer just noticed it with that revision) is that it was communicate that the answer is important for the person asking it. Whether or not it was the case in this case, I think this can make a relevant difference. (At least it does for me. If I get the impression the questioner really cares this a completely different situation than when I get the impression the questioner just asked because, well, why not ask an MO question.)
Yet I (too?) think the better way to cumminicate this, is to write this personal motivation.
Other ways are bounties (of various kinds).
However, perhaps one should not completely disregard the 'other side'. Some people might simply really want to offer something for the help/information.
(Edit: sorry for posting this initially essentiallt identically twice by a stupid error)