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My thoughts: I think the main purpose of the question is very appropriate given other (usually CW) questions on MathOverflow.But the reason I think the question is worth keeping open is that it's not just another "I don't really grok Choice" question. Namely, already there are examples mentioned (Hex, Ramsey theory) that are not just about Choice.
I would probably make the question community wiki if I were asking it. I don't strongly care, but I wish that CW questions were also ones where the community was encouraged to wiki the question. Then it would be easy (well, more polite, anyway) for someone like me to go in and improve the question --- or Qiaochu in an answer requested that the question be clarified, and if the question were CW, then it would be, I think, perfectly polite for Qiaochu to simply clarify it himself.
Since I voted to close, let me briefly describe my take on the question:
I thought it was a natural question to ask, and it reflects well on the questioner that he wants to understand such issues, but it seems premised around a lack of expert-level command of issues like constructiveness, effectivity, choice....So it struck me as not being a "research-level question" and thus more appropriate on other sites than ours.
(The fact that people have said some amusing and enlightening things in response was not enough to stop me from voting to close. This is a familiar issue to followers of meta discussions. A summary of my opinion on this might be: if you ask any question to a large group of expert mathematicians, there is a non-negligible chance of getting interesting answers. But in the long run one encourages and supports interesting, pertinent and useful answers more by encouraging people to ask better -- e.g. more focused and precise -- questions.)
The OP writes in the question that they want it to be CW, so I don't see why you couldn't just edit it to make it so. (Adding a note or comment that
you did so.)
Dear Matt: my impression is that CW condition can only be imposed by the original poster or the moderators (or the multiple editor/multiple edits rule). So I am not sure if Theo has the power to do that.
Sorry for suggesting the impossible!
@Jon: Hmm. I'm not completely comfortable suggesting that one needs to have "expert-level command" (yes, I am aware that I am quoting you quoting me!) on whatever she is asking a question about. It is more than natural to ask questions about things which do not lie at the dead center of our expertise (you can try asking questions the other way, but the problem is that you might as well try to answer them yourself!). Certainly one of the express purposes of MO is to take advantage of others' expertise: we hope that what is a not so easy question for us will be absolutely immediate for someone else.
The point though is that you have to have a certain level of knowledge in order for it to be profitable to ask the real experts about it, rather
than just reading a basic text on the subject, taking a class, and so forth. So I guess that's what I really meant here: if you just read more about these things and talk to your friends and your instructors, you'll probably get answers in a much more organic and useful way than having a bunch of research mathematicians weigh in on the matter.
Anyway, I don't want to discourage you -- from your response it sounds like I didn't, which is a relief. Please do continue to think about such questions...the road to MO-level expertise is not as long as one might think.
There is a mean way for me to make anything CW: If I make enough edits to it, it becomes CW by default. But I consider this "feature" a bug.