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When I look for the review queue I can see a section called "Low Quality Posts" where I'm invited to vote and I have four options: "Looks OK", "Edit", "Close", and "Skip".

On the other side, when I flag an answer as having low quality, I get a message from the mods which can be "helpful" or "declined - a moderator reviewed your flag, but found no evidence to support it".

So, in the end who decide if a post is of low quality: the mods or the community?

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    $\begingroup$ The "helpful" status can come from the review queue as well. For example, if the post was deleted or closed. $\endgroup$ – Asaf Karagila Dec 25 '14 at 17:55
  • $\begingroup$ @AsafKaragila Thanks. However, I'm more interested on when it is declined. $\endgroup$ – user26857 Dec 25 '14 at 18:00
  • $\begingroup$ I know that you are, that's obviously the crux of the question. I'm just saying that "helpful" messages are not necessarily a message from the moderators (although "declined" are always from them). $\endgroup$ – Asaf Karagila Dec 25 '14 at 18:03
  • $\begingroup$ @AsafKaragila Good. Then maybe you know how they decide to decline such a flag, because I suppose the mods are not specialists in all branches of maths. $\endgroup$ – user26857 Dec 25 '14 at 18:26
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    $\begingroup$ I don't know how they do that; and I have plenty of complaints about regular users clearing obvious nonsense as "Looks OK" or deleting things which are reasonable. But what is the alternative? All the axiom of choice flags fall on the axiom of choice experts? All the algebraic topology flags falling into the laps of the algebraic topology experts? I don't think any expert will want to join a site like that; and those who are already here will probably leave. $\endgroup$ – Asaf Karagila Dec 25 '14 at 18:28
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    $\begingroup$ @user26857 Three pertinent facts: 1. Most posts flagged as being "low quality" concern a very little part of mostly elementary mathematics. 2. "Low quality" is not the same thing as wrong. 3. We do sometimes not act, simply because we are unfamiliar with the relevant mathematics. $\endgroup$ – Michael Greinecker Dec 25 '14 at 19:20
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This is similar to Who is handling Very Low Quality flags? on Meta.SE, but it's good to have a local version, so here is my take on it.

who decides if a post is of low quality: the mods or the community?

Either one can happen: the VLQ and NAA flags are shown in both Low Quality Review Queue and in the moderator flag queue. Here is how it works:

  1. VLQ and NAA flags immediately enter the mod flag queue in all cases
  2. VLQ and NAA flags on posts that have not been previously reviewed and are not closed, deleted, locked or accepted will enter /review/low-quality-posts.
  3. If review completes successfully, the flag is marked handled and removed from the mod flag queue
  4. If all mod-flags on a post are dismissed from the moderator flag queue, the review task is invalidated [that is, the post is removed from the queue]
  5. If the outcome of review is deletion, and a post's score prevents it from being deleted, the original flags will be marked "helpful". In these cases, and in cases where the flags are disputed, a new, moderator-only flag will be raised on the post.

The coexistence of items 1 and 2 is somewhat uneasy. There is a popular feature request Hide "not an answer" and "very low quality" flags in the moderator flag queue (made by a Stack Overflow moderator), but it hasn't been implemented yet.

The message "a moderator reviewed..." indicates the flag was handled by a mod. Flags can also be marked helpful, disputed, or declined based on the votes of the reviewers; the thresholds required for these outcomes are not clear to me. See below.

At present, with new moderators learning to handle flags, I'd expect them to try handling a few more than usual. But generally, VLQ and NAA flags should probably hang out there for a while to give reviewers a chance to deal with them.

Criteria

VLQ and NAA flags are not for indicating that an answer is wrong: that purpose is served by votes and comments.

  • NAA: user did not attempt to answer the question
  • VLQ: this may be an attempt to answer, but it's incomprehensible due to formatting or language issues.

One should be able to evaluate both of these without being an expert in the particular branch of mathematics.

An additional point here: while moderators know the type of flag (VLQ or NAA), the reviewers do not. From their viewpoint, the issue is: should the post stay or go? (Not "does the post match the definition of the flag".) This is somehow a broader issue, and so a broader range of factors enters their consideration.

The system isn't perfect, but it works well most of the time.

Technicalities

According to the original specs of current LQ review a flag should be declined if the majority of reviewers vote against it. It's possible that this was changed to "if all reviewers vote against the flag" later on, as SE kept tweaking the review process. At least we have recent evidence that closeflags can be declined by Close queue reviewers when everyone votes Leave Open. (However, there is no flag annotation in this case.)

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    $\begingroup$ I continue to be impressed by your knowledge of the SE framework. Astounding :). $\endgroup$ – Lord_Farin Dec 25 '14 at 21:55
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    $\begingroup$ @Lord_Farin I suspect that Behaviour is really a sock puppet of Shog9. :P (kidding, of course... but only slightly) $\endgroup$ – apnorton Dec 25 '14 at 23:31

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