The issue of when to vote to close has been one of the most debated topics here (deservedly so, I think). As the number of users with sufficient rep continues to increase, this issue will only become more important.

I would like to ask a question / start a discussion about one aspect of this issue:

Suppose that you have the capability to vote to close. It follows that you also have the ability to downvote. What circumstances are appropriate for each activity? Especially, when is it appropriate to downvote but not to vote to close?

I think it will generate a better discussion if I withhold my own (at any rate tentative) opinions on this until later on. But one thing I have wondered about recently is the phenomenon of "pile-on downvoting": e.g. this question

http://mathoverflow.net/questions/15214/is-0-1-a-banach-space-closed

is one which got answered in the comments (a sign that it is not a great MO question, but also that it made sense) and quickly closed. It currently stands at -7, so has garnered at least 7 downvotes. I can understand downvoting a question until it hits -1, but is there a reason to keep voting down questions like this? Note that this was the questioner's first (and only, thus far) MO question, and has rep. must have stood at the lowest possible 1 before most of the downvotes came in.

I am interested to hear what you have to say...

Possible duplicate

For what it's worth, I'll slightly expand what I said in the other thread.

You should vote to close if you think the question needs to be taken out of circulation (i.e. people should not post answers) for some reason. Typically the reason will be one of the following.

1. The question doesn't belong on MO (e.g. it's off topic, argumentative, or too discussion-y). In this case, the question probably won't be reopened.
2. The question is ambiguous. In this case, the question should be closed until it's cleaned up and then it should be reopened. Until it's cleaned up, people should be prevented from guessing what the question is and answering those guesses. Not only is it frustrating to guess what the person was asking, but it's also frustrating to read answers like "If you meant this, then your question is trivial. Maybe you meant something else." Worse, such answers prevent the question from being cleaned up because it would make the answers look outlandish for lack of context.
3. The question is too broad. This is really a special case of (1) (and perhaps also of (2)), but I feel like emphasizing it for some reason. If the question can reasonably be answered, "read the Wikipedia page, the nLab page, a book or expository article, or search Google" then it should be closed. If the asker has done these things, then he should explain how the resources he found were lacking and what else he hopes to get out of asking the question. There's no sense in asking people to reproduce large chunks of easily accessible material.

You should vote a question down if you think it's a bad question. Sometimes you'll both vote to close and vote down, but it can happen that a question doesn't need to be closed yet is still a bad question. I think I've downvoted a couple of [big-list] questions because I thought it was stupid to compile a big list of whatever it was, even though the question was fairly to-the-point and on-topic ... it's hard to bring an example to mind. On the other hand, it's pretty common that I think a question should be closed, but I don't want to vote it down. Perhaps it doesn't belong on MO, but is a perfectly interesting question, or perhaps it's ambiguous, but is probably interesting. I don't think I've ever voted to close and voted up a question.