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Answering your own question is fine, even posting a question for sake of answering them is fine.

However from time to time there are users which post questions, which for themselves would be reasonable, for the sole purpose of attracting discussion and then posting their "correct" answer.

I was wondering if there was some consensus that moderators are to be allowed to close/lock/delete these questions without let or hindrance.

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    $\begingroup$ Can you give an example topic (maybe a in search view? ) where this happened? Or an explicite example, if this is not too much of finger-pointing... $\endgroup$ – draks ... Jan 23 '13 at 10:35
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    $\begingroup$ How can a moderator tell that a question falls into this category? The only criterion I can extract from your question is that the OP did so in the past. This looks like locking a user rather than a question. $\endgroup$ – user53153 Jan 23 '13 at 13:25
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    $\begingroup$ @5PM: Well, it is mainly for cases where the user already has a sore reputation. Obviously, other cases are not obvious soapboxing! $\endgroup$ – Asaf Karagila♦ Jan 23 '13 at 15:25
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    $\begingroup$ One time I posted an question and after two days I found it answer, hence I posted the answer. How do you know (for example) that this is not the case? $\endgroup$ – Tomás Jan 23 '13 at 20:37
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    $\begingroup$ @Tomás: It is almost always the case of soapboxing when the author is somewhat belligerent and there is a lot of fuss in the comments. In any case I speak about "repeated" offenders where this is obvious. As I wrote in the first line, there is no problem answering your own question, and no problem in asking for the sake of adding an answer. There is a problem when this is used to argue against or in favor a particular idea. $\endgroup$ – Asaf Karagila♦ Jan 23 '13 at 20:48
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    $\begingroup$ @Tomás: Did your question receive what the vast majority of mathematicians would consider correct answers before you posted your own answer? Did you proceed to criticise these answers as somehow missing some great insight into the nature of mathematics? Did you inquire of others whether they know the limitations of their mathematical knowledge/ability? $\endgroup$ – user642796 Jan 23 '13 at 20:58
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    $\begingroup$ @Asaf: level number omega in a tree of real numbers represented by bit sequences and belief of the vast majority is mathematics in your opinion? I do not share it. Regards, WM $\endgroup$ – user29503 Jan 23 '13 at 21:47
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    $\begingroup$ @Wolfgang: PleSe avoid discussing mathematical issues here. This include whether or not one mathematical concept or another is accepted. Thank you, $\endgroup$ – Asaf Karagila♦ Jan 23 '13 at 22:02
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    $\begingroup$ @WolfgangMueckenheim: as Asaf said, meta is for discussing how this site functions, not for opinions about the mathematical society at large, nor for questions about actual mathematics. Please stay on topic. I've removed one of your comments since in addition to being off-topic it also contains some not-so-nice language. $\endgroup$ – Willie Wong Jan 24 '13 at 11:41
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    $\begingroup$ On principle I prefer to minimize the moderators’ summary powers, so I’m not in favor of the proposal. Sympathetic, but opposed. $\endgroup$ – Brian M. Scott Jan 28 '13 at 23:01
  • $\begingroup$ @Brian: Do you have a better solution, for when a user repeatedly posts crap which gets closed and deleted (but not immediately, sadly)? $\endgroup$ – Asaf Karagila♦ Jan 28 '13 at 23:02
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    $\begingroup$ I consider living with it $-$ i.e., the status quo $-$ preferable. $\endgroup$ – Brian M. Scott Jan 28 '13 at 23:05
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    $\begingroup$ @Brian: While I do agree that change is bad, adding crap over crap to the site is also a form of change. I was very glad to see that the moderators took a stand against it in the recent events. $\endgroup$ – Asaf Karagila♦ Jan 28 '13 at 23:08
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    $\begingroup$ I don’t object to change per se. $\endgroup$ – Brian M. Scott Jan 28 '13 at 23:12
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    $\begingroup$ I agree with @Brian: I would find it uncomfortable if I were to asked to be a judge of whether a post is "soapboxing" or not. Note that this is different from dealing with a user who repeatedly exhibit behaviour to which the community disapproves (through flags or votes). Preemptively dealing with soapboxing requires the moderators to judge the quality of content and to infer intent of the OP, both of which goes beyond decisions based on simple facts. $\endgroup$ – Willie Wong Jan 29 '13 at 13:55
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The FAQ states

If your motivation for asking the question is “I would like to participate in a discussion about __”, then you should not be asking here.

I think it can sometimes reasonably be inferred that a user posts a question for the sole purpose of generating a discussion even if the same question could be interpreted as an honest one in a different context. The situation you describe is one such case. It should be especially clear that MSE is not a playground for voicing odd opinions on mathematics, probably the least controversial of all subjects. Such questions should be swiftly closed and deleted. Cranks have managed to kill online mathematics communities before.

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    $\begingroup$ +$\omega_1$ on that last sentence. $\endgroup$ – Asaf Karagila♦ Jan 23 '13 at 8:54
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    $\begingroup$ @AsafKaragila: how does that differ from a finite vote? $\endgroup$ – robjohn♦ Jan 23 '13 at 9:13
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    $\begingroup$ @robjohn: Well, for one thing a particular crank will dismiss this as a fallacy, and therefore no vote at all. :-) $\endgroup$ – Asaf Karagila♦ Jan 23 '13 at 9:41
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    $\begingroup$ @robjohn: The real question is if you consider the collection of all finite sequences of votes, does a $\omega_1$ vote appear in the sequence. And why do you think so? Note that the $\omega_1$ vote does not differ from a finite sequence of votes in any of its finite initial segments. And this is a very dangerous question to be asking here. $\endgroup$ – user642796 Jan 23 '13 at 12:04
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    $\begingroup$ But, Michael, Asaf didn't ask whether the question should be closed and deleted, but whether the moderators (meaning a majority? or meaning any one moderator?) are allowed to close and delete. One could take the point of view that the membership at large (those with enough points, anyway) should do the closing and deleting. So I think your answer is not an answer. $\endgroup$ – Gerry Myerson Jan 23 '13 at 12:19
  • $\begingroup$ @GerryMyerson I think it was clear that I support moderator deletions. $\endgroup$ – Michael Greinecker♦ Jan 23 '13 at 12:23
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    $\begingroup$ @MichaelGreinecker You mean, the deletion of moderators? Ouch! :-) $\endgroup$ – Did Jan 23 '13 at 15:24
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    $\begingroup$ @Did This democracy stuff is still all new to me. $\endgroup$ – Michael Greinecker♦ Jan 23 '13 at 15:25
  • $\begingroup$ @Michael: "mathematics, probably the least controversial of all subjects"? Nothing could be more controversial - at least with respect to the present state of mathematics. Regards, WM $\endgroup$ – user29503 Jan 23 '13 at 17:53
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    $\begingroup$ ...and some cranks are like herpes. They have seasonal outbreaks. Usually when the academic year is out, and they have way too much free time. $\endgroup$ – Asaf Karagila♦ Jul 8 '14 at 15:58
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You are asking whether a new category of closable postings should be created, not as part of the visible close/reopen process, but as an invisible moderator power that circumvents the ordinary user decisions.

It seems to me that at least two conditions have to be met before any such changes should be considered:

(1) There is a serious and recurring problem,

and

(2) solutions of this problem must be immediate to be effective.

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