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After spending quite a bit of time trying to crack a problem about the convexity of a multivariate function by myself, I asked this question a couple of days ago: Convexity of difference of log-sum-exp: $f(x_1, x_2, x_3, x_4) = \log(e^{x_1} + e^{x_2}) - \log(e^{x_1} + e^{x_2} + e^{x_3} + e^{x_4})$.

A user (one of the top users in the math.SX community) did a great job helping me find the answer. I actually learned a useful lesson: when trying to analyze convexity of a multivariate function, start by restricting yourself to a subspace by fixing some parameters.

This user, however, instead of writing an answer, solved the problem in a comment. When I suggested him to transform his comment in an answer, he suggested me to delete it (and it correlated with a downvote on my question, although I cannot know for sure it was him / her).

I'm fairly new to the math.stackexchange community, so perhaps I misunderstood the kind of questions that are expected here. I read Differences between mathoverflow and math.stackexchange., which states that math.SX is a

Q&A site for people studying math at any level & professionals in related fields

My question is definitely not research-level, and turned out to be fairly simple to solve (it always seems obvious once you have the answer...)

Even though it might seem very ad-hoc at first sight, the question is motivated by the general form of the likelihoods of some statistical models of comparisons / choices, such as elimination by aspects and paired team comparisons. (Note that I did not talk about this connection for now in the question - this could certainly improve it).

So my questions are:

  • is the type of question I asked not welcome on math.SX?
  • if not, why exactly?

The comment "because it's of no use to others" seems a bit subjective. I certainly know other people who would be interested in this question & answer. Perhaps "not enough others"? But what is enough?

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    $\begingroup$ Seems fine to me. That user's behavior is really strange. $\endgroup$ – Deusovi Jun 29 '16 at 11:30
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    $\begingroup$ "he instead downvoted my question" You do not know. "and suggested me to delete it." Yeah, and asking them for their reasons was not an option because...? (Relatedly, I see you did not mention this meta post to the user who helped you on main, although you are basically questioning publicly their actions. What do you think of this approach?) $\endgroup$ – Did Jun 29 '16 at 11:57
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    $\begingroup$ @Did fair point about the downvote - will edit the question. Also, i will mention this meta post. Note that I'm grateful for his help, and this meta post is about trying to understand what fits on math.sx and what doesn't - not questioning his actions (as I said (s)he's a top user, and certainly knows better). $\endgroup$ – lum Jun 29 '16 at 12:04
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    $\begingroup$ Some users have extremely conservative / strict ideas of what is worthy content, and will downvote and delete everything that does not meet their standard. You happen to have encountered a user on the most extreme end of that spectrum, as is clear from his 200 upvotes vs. 48000 downvotes (1/8 of all downvotes on the site). Most MSE users are not like that, so don't let that give you the wrong impression of the site. $\endgroup$ – Bill Dubuque Jun 29 '16 at 15:50
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    $\begingroup$ I agree completely with @BillDubuque. I think your question is perfectly fine and your online demeanor is polite and appropriate. I recommend that you that your paraphrase his response as your own answer. You can always mark your answer as Community Wiki, if you are uncomfortable with that. $\endgroup$ – Mark McClure Jun 29 '16 at 16:22
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    $\begingroup$ In fairness, I guess I would add that the commentator did not call the question "bad"; he said "it's of no use to others" - presumably, because it is of a fairly narrow scope. I also think it's reasonable for him or her to decline to expand their comment into and answer, if they simply aren't inclined to do so. $\endgroup$ – Mark McClure Jun 29 '16 at 17:09
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    $\begingroup$ Seconding what Bill Dubuque says. I am quite a bit further along the spectrum than he is, but I still find the comment that the question should be deleted weird, as I too find it to be a fine question. $\endgroup$ – Tobias Kildetoft Jun 29 '16 at 18:15
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    $\begingroup$ It may be worth noting there is no vote to close on the question. $\endgroup$ – quid♦ Jun 29 '16 at 18:37
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    $\begingroup$ Iirc there was a vote to close. It seems to have been retracted. $\endgroup$ – Bill Dubuque Jun 29 '16 at 23:31
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    $\begingroup$ IMHO, the question itself is fine but phrased in a way too specific to be useful to others. It is possible to construct an answer for it which are useful to the others but the return/effort ratio will be low. Personally, I won't mind that question remains or get deleted. $\endgroup$ – achille hui Jun 30 '16 at 2:49
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    $\begingroup$ Thank you for all your comments, it's very appreciated. As soon as I get a chance, I will answer to my original question and mark it as community wiki. $\endgroup$ – lum Jun 30 '16 at 7:42
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I think your question is fine. The user who asked you to delete it has extremely high standards, as mentioned in comments.

I am fairly conservative as well (I am the 7th highest downvoting user, with more than 1% of all downvotes site wide), and yet I upvoted your question and think it is fine.

If I had to posit a guess why the user didn't think it would be useful, it's because it's fairly localized. For example the question "what is 4343434.22 plus 454522194?" would not be good. Your question is about a specific function that is unlikely to come up again.

However your question is well worded. You are polite. You show research effort. The answer (set $x_1=x_2=x_3=0$) is applicable to other situations. For those reasons, I think this is a good question and should stay on the site.

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    $\begingroup$ Tangentially, it is not clear to me why "conservative" would be a good adjective here. It does not strike me as descriptive. Being conservative might mean that one wants to keep around (viz. conserve) all content, preferably unchanged. Being conservative might mean being against changes and developments of the site's policies. Or various other things. $\endgroup$ – quid♦ Jun 30 '16 at 23:39
  • $\begingroup$ @quid I mean "wanting to conserve the integrity of the site/question quality", to put it somewhat grandiose. Or as an antonym to liberal/"permissive". $\endgroup$ – user223391 Jun 30 '16 at 23:46
  • $\begingroup$ Yes, I understood that from context. But, it seems not descriptive in itself. $\endgroup$ – quid♦ Jun 30 '16 at 23:59

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