This is a meta meta question on the principles by which we should decide which tags to create. The motivation for the question stems from this meta discussion, in which a majority thought that there shouldn't be an errata tag, whereas a significant minority of $5$ upvoted my answer saying there should be one. Usually that would be the end of it, but after answering yet another errata question I thought again that it's a pity that I can't categorize these although I think it might be useful, and that made me wonder whether there should be symmetry here between votes in favour and against.

This hinges on what the cost of tags is to those who don't find them useful. In the limit where there's no cost, one person who finds a tag useful should be enough to create it and all votes who find it useless should be irrelevant, whereas in the limit where the cost is high, the decision should be by a straight majority vote. Now I'm obviously biased because I'd like this tag to be created, but it seems to me that the cost of creating one more tag isn't very high. We currently have $538$ tags, including quite a number of empty ones, some rather hyper-specific ones like "vapnik-chervonenkis" and slightly informal ones like "simplicial-stuff", and a full quarter of them don't have more than the $4$ questions tagged that I alone could tag right away as relating to errata.

Also, the main use of tags is to be able to find things, either by searching or by following certain tags that you're interested in. Neither of these is in any way affected by there being more tags in total or by individual questions being tagged with more tags -- the more, the merrier. The only scenarios I can think of where it might incur a cost to have more tags is (a) if you're looking at the tags for a question to decide what the question is about and there are so many tags that you can't tell at a glance, and (b) if you're browsing the tags deciding which ones to follow and there are too many to get an overview. (a) seems unlikely to me; (b) might be a problem, but it seems that with $538$ existing tags it's not going to get much worse, and the only solution for that is to browse the more frequently used tags, and of course if the new tag were to get in the way by becoming one of the more frequently used tags then it should have been created anyway.

So my questions are: Where do you see the cost of creating new tags? How high is it? Do you think it's high enough that a tag shouldn't be created when $5$ people see a use for it and $9$ don't?

P.S.: I just noticed http://meta.math.stackexchange.com/questions/2466/new-tags-when, which is on a related topic. (It hadn't shown up in the "questions with similar titles" list). I'm leaving this one open though because it has a different focus. In the case with which that thread mostly deals, splitting or merging general or specific tags, there's an additional cost in that too specific tags might prevent questions from being tagged with the less specific tags (though ideally that should be prevented by a tag hierarchy); that's not the case when a tag like "errata" isn't a subset of an existing tag.

P.P.S.: Another candidate for the "errata" tag just came up: Substitution in ODE.

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    $\begingroup$ +1 Make that a minority of six. I just read the related post, and this post and the ensuing...I agree, joriki, that this tag would be useful. Just my two-cents. $\endgroup$ – Namaste Aug 24 '11 at 2:09
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    $\begingroup$ To add on amWhy, make that seven. Which coincides with the first part of The Magnificent Seven which I have watched last night. $\endgroup$ – Asaf Karagila Aug 24 '11 at 12:24

Some tangential stuff about your post, but no answers to your main question.

A few things which must be added into consideration:

  • Tags with low usage will automatically be removed after 6 months.
  • "Empty" tags do not persist over night: tags which refers to no questions are removed from the database every night.
  • What you perceive as "empty tags" in the tags listing may in fact be tags which are synonyms of other things. Those tags will show up in the list of tags, but will not have a listing of number of questions.
  • Each question is only allowed 5 tags. So over specification can lead to a scenario that actually makes questions harder to find, because a question will not be able to contain every single possible applicable tag.

I don't think the VC tag is appropriate: it is way too specific. If I had seen it when the question was first asked, I may have just removed it. It is likely to be removed by the low-usage tag clean-up process anyway.

I am not sure if you are familiar with the simplicial-stuff tag. It is not "informal" as you suggest, and is probably the best way to describe the subject.

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    $\begingroup$ Thanks for the details on how the tags work. Where do you find out about this sort of stuff? Those were offhand examples; the main point was that there's a large number of tags that aren't used more than "errata" would be right from the start. I didn't know about the clean-up process. What's the threshold for that? Regarding the limit of five tags: Of the four questions I'd currently like to label as "errata", three have one tag and one has three. There are no questions with five tags in the "active" view currently. If there's ever a conflict, one could still apply the five most useful tags. $\endgroup$ – joriki Aug 24 '11 at 7:54
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    $\begingroup$ I was searching on meta.SO what exactly low usage means; it seems that tag having only 1 question is going to be deleted after 6 months: meta.stackexchange.com/a/48418 Another related meta.MO question: What happens to zombie tags? $\endgroup$ – Martin Sleziak Jan 6 '12 at 13:18
  • $\begingroup$ A small addition to the information provided in the links in my previous comment. Single occurrence tags are now removed by the automated process only if they do not have tag-wiki. $\endgroup$ – Martin Sleziak Apr 22 '17 at 7:44

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