Somewhat often someone will ask a "borderline" question on MO. These tend to result in much discussion on meta. Often we will close such a question, despite it being somewhat controversial. This is especially easy now that a lot of people have the ability to vote to close. What I'm going to argue for here is that we *should not vote to close borderline questions*. (We should, of course, still quickly vote to close questions that are obviously not appropriate. The big upside of having so many 3K+ voters is that we can close very bad questions really quickly.)

Here are my reasons:
1) There aren't borderline questions frequently enough for them to cause a problem. If a particular sort of borderline question starts to become a problem we can deal with it then.
2) Closing questions can lead to unhappiness, so we shouldn't do so without a good reason.
3) Sometimes questions that appear "borderline" actually are excellent questions if the right person happens across it. The recent laTeX controversy is a good example (http://mathoverflow.net/questions/22141/how-do-i-see-latex-math-on-any-web-page). If you reason to vote to close is "MO probably doesn't have the right people to answer this question" then I think instead of closing you should just wait to see if the right person happens to show up.
4) By letting a few more borderline questions get through we'll be better informed about what does and doesn't work well on MO.

Thoughts? Comments? Disagreements?

I agree

I agree with this sentiment, although it is hard to make precise. (We will not all agree on whether a question is borderline.)

One argument in favor of this is a procedural one: IMO, it is a serious flaw in the current system that we cannot vote to close and open at the same time. Currently a question can get closed even though the vast majority of MO "citizens" (>= 3000 rep) would like it to stay open. Then it goes through a reopening process which -- as we have recently seen -- may not be swift enough for the person who is annoyed that their good question got closed. I am waiting for the question that gets closed, reopened and reclosed. Isn't that just a matter of time?

I am also really coming around in my opinions about "straightforward" questions and questions which "look like they could be homework", but that's a separate thread.

The way I feel now is that if someone asks a coherent, precise question that pertains to university-level mathematics at the theoretical / conceptual level [i.e., asks for a proof rather than just a computation], we should be reluctant to close it. The answer may be something like "Look in this standard text", but what's wrong with that?

I think it's important to call some attention to borderline questions if we want to see the benefits of (4). So I agree with Scott that the right thing to do if you think a question is borderline is to leave a comment saying so and start a new thread on meta. If you do this, I don't think it matters whether you vote to close. Once there is real discussion about a question (someplace more hospitable than the comments), I think we'll quickly come to a consensus about whether the question should be open or closed. And if we don't, I'm happy to leave the question open.

In the long run, the "don't close borderline questions" strategy simply won't work. Once there really a lot of people who can vote to close, it just doesn't make sense to say "don't vote to close borderline questions" because people will disagree too much about what is a borderline question. But that won't be too big a problem because we'll have enough high rep users to reopen questions swiftly.

Just a quick example: I notice this question has been up for 20 hours, and has only 3 votes to close (one was mine). I am curious if it is because people consider it borderline?

That question is closed now, but I didn't get the chance to vote to close it. I left this comment:

I was also going to vote to close. It could be that there's some big gap in my education, but I can't make much sense of the question. My guess is that you're trying to maximize $x_1$ subject to the condition that $x_1$ is less than $\delta$ and less than $0$, but some English explaining what you're actually trying to do would really help. As is, it seems like you're just trying to compute $\min{0,\delta}$.

Please speak up if you feel like this is not a good reason to close (or to tell me that I don't know anything about linear programming and I should go away).

Expanding on my earlier thought...

Closing borderline questions is not all that bad. Borderline questions attract borderline or worse answers, which will actually undermine the question. For example, if the question is slightly argumentative then it is likely that someone will pick up on that and start an argument. If the question is too imprecise, then it might get divergent answers and correcting the question becomes very awkward. Closing the question prevents situations like that to happen: no answers can be posted until the question is reopened.

I think that if we stop thinking of closing questions as a negative judgment, and we make that clear to all users, then the process can start working smoothly.

In the case of 22569 can we combine the questions and reopen?

@Andy Putnam: +1, I completely agree.

I don't think it is snobbery (or, if it is, it is a form of snobbery that I endorse). One of the things that I have tried to bring up from time to time on meta is the following principle:

MO is a subset of the worldwide community of research mathematicians. It is not a rival community. Therefore when a conflict arises, it is more important to maintain the ethics and social mores of the former community than any MO-specific ethics. This includes treating people who are established with great respect. (As I have also said before, if you find it too hard to figure out who deserves great respect or find giving great respect to famous mathematicians too much of a double standard....then just treat everyone with great respect. There's no harm done!)

@fgdorais:

We shouldn't think of it as being negative? That'll lead to the same problems we've been having. We should think of it as being serious and insulting, and reserve it for only the worst cases.

Everyone warns of the front page being crowded with crap, but I haven't seen any evidence of that. As long as we prevent crackpots and people with service course level problems from posting, I don't think we'll have any problems.

Andy, I think out points of view are not in complete disagreement. We both agree that what is necessary is for us to act in a more measured way when closing questions. The problem appears to be that we are too trigger happy when closing questions, which led to the "thought police" criticism.

This argument has a long history, Emerton and Pete proposed the "preferred user approach" in this thread. Although I understand the need to be welcoming to highly qualified users, I completely disagree with this idea: all discrimination policies are bad.

My point of view is that we should always motivate our closing votes, no matter who is asking the question. We're actually pretty good at doing this with homework and elementary questions. One of the five voters usually posts a comment with a link to the appropriate section of the faq. Why can't we be as thoughtful in other cases? I really liked Hailong's comment to this recently closed question. I think that if we were always this nice, then the "thought police" might not be perceived in such a bad way.

There is no trivial reason to close a question. As a community of mathematicians, we suffer from some side effects of our profession, especially our disdain for trivialities. It's obvious that "left as an exercise to the reader" is not a valid explanation for closing a question, but we sometimes think that "this is off-topic" is sufficient. It's unreasonable to assume that the poster will immediately wonder why their question is so clearly off-topic, as one would when reading another not completely transparent assertion in a paper. The reasons for closing a question should be completely transparent in every case.

As I think about this, the more I realize how bad my own behavior has been. I think we could all use a moment of reflection on this subject.

My problem isn't so much with these "borderline" questions, it's with questions that come across as insufficiently motivated, or which haven't given enough thought as to what a desired answer might be. Mais chacun a son gout, to some extent at least...

I would also rather judge questions by their tone and not their subject, if that makes sense.

If it's a bad question from an unknown(google) with 1 reputation, I still think that we should still close it.

I think the goal of closing questions is to eliminate questions which are 1. completely inappropriate (eg the question about why mathematicians are stuck up that was posted recently), and 2. obviously low-level homework, like calculus or linear algebra or trivial group theory.

There are other reasons to close a question. For example, as Yemon was saying, vague questions should be closed since they do not disappear from the front page: they torment important people in the MO community and they typically get edited after they've gotten a few answers, making the answers non-nonsensical, to everybody's annoyance. See this post of mine for more on this.

For another example, fluffy (usually [big-list] or [soft-question]) questions should often be closed. A certain density of such questions is okay, but too many of them makes the site annoying to people trying to do some real mathematics. See these threads for more on this.

For a third example, discussion questions should often be closed. A discussion question may seem like a good idea, even to an actual mathematician, but they are actually extremely frustrating to have on MO. See all these threads for more on this.

I think it makes sense to regularly re-evaluate our reasons for doing what we do, but we should at least look back to see what our reasons were in the first place. If we're going to do that, then we'd better also leave a record of what our new reasons are so we have some wisdom to lean on down the line. That's why I'm really stressing that "borderline" questions should become threads on meta. If we decide to just leave everything that's not blatantly offensive or a homework question open, then we'll end up with a sucky site and we won't even know why.

this would have to be reevaluated if there was a sudden flood of crap questions, but I see no evidence that will happen.

See the two threads I linked to above relating to "fluffy" questions for examples from MO history where people felt like there was a flood (or at least a substantial trickle) of irritating questions which were not homework, and were even kinda on topic.

Let me throw something else into the mix. Suppose that there is a question that I feel is a bit borderline. Maybe it's a little vague, or a little argumentative. Perhaps I can see that it could be interpreted in two ways: one which would be okay, one which wouldn't be. Not wanting to see the "bad" interpretation, I vote to close, leaving a note as to why I thought it should be closed. Maybe, instead, I should have edited the question so that the "good" interpretation is the obvious one.

Which is worse: having your question closed, or having it edited?

Andrew, that's an excellent question!

In principle, edits should only be done only when you are sure that you are preserving the meaning of the question. In the cases you describe, the intent of the edit is to change the meaning, but I think this is sometimes justifiable. A concrete example of this is when I edited the first paragraph of How do I see LaTeX math on any web page? My edit was substantial enough that I did change the meaning of the original question. My reasoning in this case was that if my edit did not preserve the intended meaning of the question, then the question clearly ought to be closed.

Also editing a question still leaves the original author in control of the situation, unlike closing which feels like someone took something away from you.

I have seen at least one user get offended when someone else made a relatively minor edit to their question / answer. I don't think this has been an issue, either because people don't notice when their questions get edited or because most people are reluctant to edit questions substantially, but it's something to keep in mind.

Hi, Folks. Have you thought of a way of contacting VA individually, saying, I imagine, that while general opinion varies among those burdened with the responsibility of shepherding MO during its initial months, it is regrettable that things worked out as they did on the Latex question, and it would be great if (he?) would resume his role in helping with the difficult algebraic geometry questions? I would have done something of the sort myself (I know, shudders of horror) but have no method of doing so. But I have the luxury of making such a suggestion precisely because I am so very far from consensus behavior, and am in little danger of ever setting policy-I have no understanding of why anyone would use a pseudonym on a website of this type, I really really like individual email, answer mine, send email to people even if they have not answered a few of mine (although I take a hint eventually), and so on. Furthermore I am in favor, in many ways, of tailoring responses to the individual. From the Jeeves and Wooster books by P.G. Wodehouse, I am in favor of considering the "psychology of the individual." Will Jagy.
Notes: (1)even from my ordinary MO account, I can see that VA has edited his Latex answer recently, but has not answered any math questions. (2) fgdorais, it was not until graduate school that I realized discrete and discreet were different words, possible typo of course.

(Thanks Will! I did not actually know that, I always thought discreet was just an alternate spelling. I learned English mostly by reading math and watching cartoons, which has strange side effects.)

(@fgdorais: typical usage on the Internet would do little to dispel this notion...)

Happily, VA has undeleted a bunch (maybe all, AFAIK) of his answers.