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A surprising kind of (a lot of) active users: Those who don't ask question.

For example:

Robert Israel 2,729 Answers, 0 Questions.

Brian M. Scott 5,847 Answers, 0 Questions.

André Nicolas 5,528 Answers, 0 Questions.

Arturo Magidin 3,329 Answers, 2 Questions.

I found it quite strange that there are high reputation users that are very active in math.SE (they probably spend much of their life in mathematics) but do not ask anything. It seems strange for two main reasons:

  • In mathematics it is very easy to find a problem that you cannot deal with, regardless of your academic level. There should be no problem asking because of the excellent quality of the site: People who frequently visit math.SE often know the high level that users have and the quality of their answers. Asking in math.SE may be the quickest and easiest way to find a solution to your question. Undoubtedly, when the "valued users" need help, an answer is a tiny way of paying for their work on the site.

  • Discussing and asking helps us to learn, we can always ask and learn more, and we very often want other people to opine on a topic in mathematics that interests us, to know other approaches.

I have two theories:

  • They are embarrassed to ask or want to maintain some type of image (in the latter case using other accounts to ask).

  • They always can help themselves or have external help.

I think I need an explanation to this so common phenomenon.

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    $\begingroup$ Why people downvoted? $\endgroup$ – Gaston Burrull May 25 '13 at 10:01
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    $\begingroup$ It really was a coincidence, I had never looked at the chat, it took me over 2 hours to put the question by my poor knowledge in English $\endgroup$ – Gaston Burrull May 25 '13 at 10:09
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    $\begingroup$ Far from me the idea to compare myself to the outstanding users you mention. But I happen to have an infinite answers/questions ratio and I don't have a real explanation for this. I guess I'm happy enough with the questions I read here. But you just made me feel like asking one sooner than later. $\endgroup$ – Julien May 26 '13 at 2:59
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    $\begingroup$ @julien: You write pretty nice answers, so a large A/Q ratio is a good thing! $\endgroup$ – Brian M. Scott May 26 '13 at 5:02
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    $\begingroup$ I for one am very appreciative of the effort that you, Gastón, and many others make to communicate in English. $\endgroup$ – Brian M. Scott May 26 '13 at 5:05
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    $\begingroup$ As a current undergraduate, you are probably not familiar with Newsgroups and sci.math.research. If you were, you'd have known that Robert Israel has been answering questions since around the time you were born. :-p $\endgroup$ – Willie Wong May 26 '13 at 10:24
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    $\begingroup$ Note that many of these users also have accounts on MO where questions have been asked. Maybe they're just too smart to ask questions of an appropriate level for MSE. $\endgroup$ – Alexander Gruber May 27 '13 at 14:28
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    $\begingroup$ @Alexander Gruber Your answer started to make sense, until the end. Math Stack Exchange is explicitly for all levels. That said, if you had just said "many of these uses have accounts on MO, so maybe they just prefer to ask their questions there, where research experts tend to congregate" I might have upvoted your answer. But, with that whole thing about "smart" that you had there... sorry, now I can't upvote it. $\endgroup$ – Doug Spoonwood May 28 '13 at 1:32
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    $\begingroup$ @DougSpoonwood Well, my dear Douglas, surely a site with "top level only" is encompassed in a "all level" site, and as such it is possible for the very smart to ask their questions here. However! Our beloved FAQ encourages research level questions be asked at MO for a better success rate, and I might point out that those of truly exceptional intelligence would think of checking the FAQ before asking the question. Therefore I stand by my previous statement, fully acknowledging that I myself in fact ask a lot of questions here. I shall consider my upvote owed, good sir! $\endgroup$ – Alexander Gruber May 28 '13 at 2:25
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    $\begingroup$ @GastónBurrull Why did you edit the question to undo a correction done by someone else? (the old version was grammatically correct, the new one is not). $\endgroup$ – Tobias Kildetoft May 30 '13 at 15:05
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    $\begingroup$ Rollback @TobiasKildetoft I thought it was another mistake. "I found it quite strange that" sounds redundant to me, and I did not remember that Jonas changed that. $\endgroup$ – Gaston Burrull May 31 '13 at 2:30
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    $\begingroup$ @GastónBurrull: Thanks for asking this question. I personally think that it is because they are Masters here. I mean RBAA. More over we can add to them, missed GONE as well. :-) $\endgroup$ – mrs Jun 3 '13 at 5:59
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    $\begingroup$ After reflection I've downvoted the question. Apparently there are some who find the question of value, but as phrased the text impugns the motives of individuals, baselessly suggesting that they have an "image" problem and engage in sockpuppetry to avoid "embarrassment". Levelling such remarks at the highest reputation members of the community is perhaps not quite so bad singling out some whose reputations are less secure, but it isn't right. Perhaps the question should be edited (or closed). $\endgroup$ – hardmath Jun 5 '13 at 15:01
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    $\begingroup$ @hardmath I don't think it's that bad. The fact that it may be a bit impugning is an unfortunate consequence to a perfectly valid question, and I think it's the valid question part that counts here (after all it's a Q&A site). The asker does a very good job at explaining the relevance of this question, especially the part about wanting to give back to them for all their contributions. It's a very good question! $\endgroup$ – Ataraxia Jul 20 '13 at 23:21
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    $\begingroup$ I rarely have questions that I cannot handle myself or with google and that are suitable for this site. Either I am looking for good examples which is frowned upon by this site or the question is more suitable for mathoverflow anyway. $\endgroup$ – Phira Apr 7 '14 at 23:58
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The second of your theories is a decent explanation, I would class myself in there. I have access to a decent mathematical library and the internet, so 95% I can find what I need quite quickly on my own. To be honest, I think many questions here can be answered by a simple google search, but I understand how some people will want the ability to ask the answerer for elaboration which is not possible for other online sources.

The rest of the time I ask an instructor, since that is what they are there for. I just find it much more convenient for several reasons that I won't go into. If I wasn't enrolled in a university and studied completely on my own, then I imagine I would ask many more questions here.

The first of your theories seems like it could be true for some users but I don't think so for users like the ones you listed. The people listed in your question are all experienced professors of mathematics and I imagine that any questions that they would find interesting and not solve on their own within several hours would most often not be the type of question suitable for math.SE but perhaps mathoverflow.

For example, Pete L. Clark has 746 answers and only 8 questions here while at mathoverflow he has 440 answers and 57 questions: A/Q ratio is 93.25 here vs 7.719 at MO. Or Matthew Emerton who has 800+ answers here but no questions, but he has 3 questions at MO. Georges Elencwajg has 845 answers and no questions here, but he has 32 questions at MO. So it's probably not about maintaining any image, they feel quite free to ask questions that everyone can see on the internet but those questions simply aren't likely to be answered well here.

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  • $\begingroup$ Thanks for your detailed answer. $\endgroup$ – Gaston Burrull May 26 '13 at 6:53
  • $\begingroup$ Excellent answer, +1 $\endgroup$ – Rustyn Oct 24 '14 at 17:30
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Has anyone entertained the possibility that some folks on this site just like to solve problems, and those posed in M.SE are an easy source of them? BTW I am one of those strange folks (> 1100 answers, 8 questions, not as extreme as those you listed, but still...) and that's one reason how I explain it.

Another reason is that I am not a student or am even in a profession where I do math as part of my job, so I have few questions to pose.

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    $\begingroup$ I had not considered that possibility, I assumed as active people necessarily work in mathematics. Thanks for letting me know the point of view of one (you) of those people. $\endgroup$ – Gaston Burrull May 25 '13 at 22:19
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    $\begingroup$ @Gastón: I've also asked relatively few questions ($15$ questions, $2410$ answers), and I also don't work in mathematics professionally. $\endgroup$ – joriki Jun 3 '13 at 6:17
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    $\begingroup$ Wow, Ron. I would have assumed you were a professor with how prolific your answer history is on here. It's pretty shocking to me that you're outside of academia altogether. If it's not too personal a question, why is that you aren't in academia? $\endgroup$ – Cameron Williams Oct 25 '14 at 5:09
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    $\begingroup$ @CameronWilliams: it's not too personal. I worked in my field for years and started hating what I was doing. (It was not in academia anyway.) I changed careers into patent law and have found myself falling in love with math all over again, because it's a fun thing to do. Maybe someday I will teach. $\endgroup$ – Ron Gordon Oct 25 '14 at 15:04
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    $\begingroup$ @RonGordon I see. Well this site has definitely benefited from your time here. You're quite talented at making fairly complicated things very easy to understand. You'd make a great teacher or professor. $\endgroup$ – Cameron Williams Oct 25 '14 at 17:48
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    $\begingroup$ @CameronWilliams: thanks for that. $\endgroup$ – Ron Gordon Oct 25 '14 at 19:47
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Let me offer a possibility.

Let us take for granted the supposition that these people who take time to write careful, well-written answers, would also exert some amount of effort in making sure they will write careful well-written questions.

The thing is, it often happens that in the course of trying to write a good question, suitable for public display, one might actually be able to figure out the answer to his question. I can't explain why it is so, but it happens.

I would then wager that it is also likely that it can and has happened that they've managed to solve their own problem(s) in the midst of trying to formulate them properly.

(Of course, anyone's guess is as good as mine.)

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  • $\begingroup$ It's pretty convincing, thanks. $\endgroup$ – Gaston Burrull May 25 '13 at 10:04
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    $\begingroup$ It's the Feynman algorithm. "(1) Write the problem; (2) think really hard; (3) write the solution." Most people, however, think it's fine to skip the first step and proceed to thinking really hard. Writing a well-written question often consists of the first step, then the second step becomes somewhat easier, and the third step follows. $\endgroup$ – Asaf Karagila May 25 '13 at 10:44
  • $\begingroup$ @AsafKaragila I must admit that while I was writing one of my last questions, trying to be as clear as possible and develop the context in the best possible way, half of my doubts disappeared, so though I have not asked all questions that I had, I answered several things to myself and some of them I wrote as development of ideas without actually asking them explicitly. Thus, even if no one had answered my questions explicit, the fact that people did not comment or could not identify errors in my development [...] $\endgroup$ – Gaston Burrull May 25 '13 at 22:08
  • $\begingroup$ [...] (which were my implicit questions) probably means that I answered myself properly. So if anyone had answered, I would have helped anyway. So part of my development in my question was useless for questions that remained (the explicit ones). $\endgroup$ – Gaston Burrull May 25 '13 at 22:11
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First off, I don't think these users are "strange". Perhaps their motives for being on Math.SE are different from yours or those of the majority, but such does not justify this qualification.

One of the most logical reasons for the observed behaviour is that these proficient contributors' questions, when they arise, will usually supersede the established literature, or at the very least the estimated answering ability of the Math.SE community (along the lines of "this question is too hard for MSE anyway, why bother asking?").

This makes them well-suited to MathOverflow, where there is a large base of experts in many fields, who are more likely to be able to provide answers to these advanced questions.

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The below is quoted from Brian's answer here:

"I’ve no doubt that for some users Math.SE is first and foremost a place to do mathematics, asking questions as they arise and helping others with theirs when they can; indeed, I’ve spoken with such users in Chat. Moreover, one can see some evidence of this in the available user data: one user, for example, has asked $106$ questions and answered $114$; another, $94$ and $122$. And of course as they arise is flexible enough to cover the possibility that for some users they simply don’t arise, so in some sense this description could fit just about anyone here. However, it’s very clear from the user pages that for many users Math.SE is primarily a place to ask questions, and for many others it’s primarily a place to answer them. Here, for instance, are some statistics from the first page of users sorted by all-time reputation:

$$\begin{array}{cccc} \text{Rep in thousands}&\text{Nr. of Users}&\text{Answers}&\text{Questions}\\ \hline 150\text{+}&3&14380&2\\ 100\text{ - }150&2&4795&55\\ 70\text{ - }100&6&15469&114\\ 50\text{ - }70&7&8981&77\\ 30\text{ - }50&18&18296&284\\ \hline \text{front page}&36&61918&532 \end{array}$$

Of those $36$ people six have asked no question, $17$ have asked fewer than five each, and one person accounts for a little over $20\%$ of the questions asked by these people.

For me Math.SE is primarily a place to teach mathematics, and the data above suggest that I’m not alone in this. The doing is part of the teaching and often contributes to my enjoyment, depending on the problem, but producing what I think is a good explanation or hint brings a pleasure that is independent of the mathematics involved. It is secondarily a place for me to learn mathematics: sometimes in order to answer a question, occasionally from another answer to a question that I’ve answered, and once in a while from an answer to a question that simply caught my fancy."

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  • $\begingroup$ This is a good point, Brian is one of the most extreme cases since he uses math.SE essencially to teach maths. Thanks for the most convincing answer. $\endgroup$ – Gaston Burrull May 25 '13 at 22:15
  • $\begingroup$ +1 for final paragraph. $\endgroup$ – Blue May 26 '13 at 4:55
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    $\begingroup$ @GastónBurrull: I think Brian is an 'extreme' case not because he uses math.SE to teach maths (as he says, he's not alone in this), but because he spends so much time doing so, which he has time to do because he is retired. $\endgroup$ – Tara B May 26 '13 at 7:45
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    $\begingroup$ Not just because he is retired: mostly because he is very generous with his time and insight. $\endgroup$ – Sam Lisi May 26 '13 at 22:09
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    $\begingroup$ Woot! I am "above-average"! $\endgroup$ – Willie Wong May 27 '13 at 8:17
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I had the infinite ratio for a long time -- about 250 answers before my first question. This is a combination of two reasons which have already been suggested.

  • I think most of my questions are a better fit for MO than math.SE. I tend to put a question on MO if I think that it needs an expert in the relevant field of math; I put a question here if I suspect that it is a clever application of material in the advanced undergraduate syllabus. MO consists almost entirely of professional research mathematicians, including many people at the top of the fields I work in (algebraic geometry and combinatorics); I don't think questions like 1, 2 and 3, for example, would be found by relevant experts here.

  • More than half the time, when I start writing a question here, I figure out the answer in the process of writing it.

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I'm not a student, so when I ask a question it's out of idle curiosity, or something I've been thinking about related to my research. I've received some excellent answers, but confess I've found the usefulness of asking questions to have dwindled over time, for a mix of reasons, including that the topics I ask about (PDEs, differential geometry, numerical analysis) are not as "hot" on this site as elementary number theory, linear algebra, or calculus; that the userbase has shifted more towards students, so the fraction of people viewing a question capable of answering it has decreased; etc.

But that doesn't stop me from helping and teaching others when I can.

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Simple,

  1. those users are damn good, and the questions they would have about mathematics are above the level of this site, and likely they know who to talk about the higher level mathematics.

  2. They belong to the Society of Erdős.

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    $\begingroup$ Weird timing sir. $\endgroup$ – user142198 Oct 24 '14 at 6:55
  • $\begingroup$ @Committingtoachallenge The new answer was added very probably because this question was recently mentioned in chat. $\endgroup$ – Martin Sleziak Oct 24 '14 at 8:05
  • $\begingroup$ @Committingtoachallenge yes, that was the case. $\endgroup$ – yiyi Oct 24 '14 at 8:55
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    $\begingroup$ I don't get the Erdos reference. He was as well-known for asking questions as for answering them. $\endgroup$ – Gerry Myerson Oct 25 '14 at 3:50
  • $\begingroup$ @GerryMyerson from wikipedia: Paul Erdős (1913–1996) was an influential mathematician who spent a large portion of his later life writing papers with a large number of colleagues, working on solutions to outstanding mathematical problems. --- What I heard of him is that he traveled to solve problems. $\endgroup$ – yiyi Oct 25 '14 at 10:11
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    $\begingroup$ Did you also see the part of the Wikipedia essay where it says, "Throughout his career, Erdős would offer payments for solutions to unresolved problems. These ranged from \$25 for problems that he felt were just out of the reach of the current mathematical thinking (both his and others), to several thousand dollars for problems that were both difficult to attack and mathematically significant. There are thought to be at least a thousand such unpaid payments, though there is no official or comprehensive list." $\endgroup$ – Gerry Myerson Oct 25 '14 at 22:39
  • $\begingroup$ @GerryMyerson I know that now from reading about him, and I was just trying to make a witty response and it wasn't very good. I just knew the guy loved to solve problems, and this site is not for problems that would expand mathematics - that would be math overflow. I could see him being like the users in the question posted, having a high score from answering so many questions here and then posting bounties on overflow. $\endgroup$ – yiyi Oct 26 '14 at 3:16
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Besides MSE, I have other accounts in some other Q&A sites. I notice that "high grade user are often not active in asking questions" is a common phenomenon on most Q&A sites, not only in MSE.

Perhaps this is the main reason:

For some practical reasons, most Q&A sites are often designed so that the rewards on answering questions are often more than that of asking questions. Like MSE, when asking questions, only someone vote up the questions can earn reputations, but when answering questions, reputations can be earned not only when someone vote up the answers, but also can be earned when OP accept the answers or when someone award bounties to the answers. The rewards on answering questions are often more than that of asking questions. As high reputation users are often very care about the upgradings, they often feel that answering more questions have greater efficiently than asking more questions. Therefore they often put much more efforts on answering questions rather than asking questions.

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    $\begingroup$ "As high reputation users are often very care about the upgradings..." - in other SE sites, maybe. Here... not so much. (I didn't downvote, BTW) $\endgroup$ – J. M. is a poor mathematician May 26 '13 at 3:53
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    $\begingroup$ Reputation is not money, there is no incentive to do that. $\endgroup$ – Gaston Burrull May 26 '13 at 4:17
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    $\begingroup$ The flood of downvotes is a reaction to what, exactly? The first paragraph is an observation that should be part of the discussion, and the rest is a perfectly good answer. $\endgroup$ – zyx May 26 '13 at 17:11
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    $\begingroup$ @zyx They are probably by people who tend to not ask questions, but for whom the reason has nothing to do with maximizing reputation. The answer is based on a guess of why some people do some things, and if those people do those things for a different reason, it makes sense to downvote. $\endgroup$ – Tobias Kildetoft May 26 '13 at 17:26
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    $\begingroup$ @TobiasKildetoft, such downvotes would basically respond to a non-English speaker's use of the word "often" when something else could have been substituted. Some high-rep users obviously care about reputation and it is surely a factor in more subtle ways for (some) others who do not necessarily care, by setting the environment in which they operate. $\endgroup$ – zyx May 26 '13 at 20:39
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    $\begingroup$ @zyx I don't see where the word "often" is used in a way that has any bearing on this. $\endgroup$ – Tobias Kildetoft May 27 '13 at 0:08
  • $\begingroup$ The sentences with "often" are the only ones that talk about high reputation users and what might motivate them, and the quantifiers turn an easily witnessed statement about some of those users into (at least in some readings) an almost universal characterization of most such users. It is this that I suppose might have caused the downvotes according to your analysis. @TobiasKildetoft $\endgroup$ – zyx May 27 '13 at 2:38
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    $\begingroup$ @zyx I might have agreed with that reading if the answer had not also said "Perhaps this is the main reason". $\endgroup$ – Tobias Kildetoft May 27 '13 at 12:23
  • $\begingroup$ Nothing in the "perhaps ... " connects to individual high rep, high A/Q users without those "often ... " quantifiers, and the only thing one could criticize in that sentence is the word "main", which is essentially the same issue as the one with "often". This answer is a correct analysis of part of the behavior, but stated in stronger terms than are completely accurate, and I think stronger than would naturally be used in the case of native English fluency (some if it may be as simple as word order differences that change the concept being conveyed). @TobiasKildetoft $\endgroup$ – zyx May 27 '13 at 12:39
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    $\begingroup$ Some users writes answers cause they like the question or their answer. And I only ask questions when I am interessted in and not for the reputation $\endgroup$ – Dominic Michaelis May 28 '13 at 21:08
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    $\begingroup$ @DominicMichaelis, of course, but a look at the user behavior on MSE and the numerous meta threads about lost or capped reputation shows that there is an effect of the reputation system on user actions, including some of the high reputation answer-only people that are the subject of this conversation. This is consistent with many users not caring at all about the reputation score. For those who don't care there still can be effects when interacting with others who do care. (Changing the name from "reputation" could help, it is grating to keep typing that when talking about the software.) $\endgroup$ – zyx May 31 '13 at 20:16
  • $\begingroup$ @zyx You're not understanding a very basic fact. The reputation is well seen only when it is well-earned. $\endgroup$ – Gaston Burrull Jun 2 '13 at 6:41
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    $\begingroup$ @GastónBurrull, you don't have any way of knowing what others do and don't understand. That second sentence is not correct: some reputation effects derive from how the points were earned, and others are independent of that, it is a combination. And whatever the truth about that matter, it would not contradict what was written. If there are people with high but "not well-earned" reputation are these not the ones who are most likely to be adjusting their use of MSE, such as answer/question ratio, to maximize reputation? $\endgroup$ – zyx Jun 2 '13 at 6:51
  • $\begingroup$ @zyx Note that downvotes at meta are not an indicator for a bad answer, but for an answer the downvoter does not agree with. In this specific case, why would you only answer questions in order to maximise a number on a website (you could play cookie clicker just as well and get many more "points"). The other answers (often from users who indeed do not ask many questions) provide a better understanding since those users know thier own incentives. $\endgroup$ – AlexR Dec 11 '14 at 22:56
  • $\begingroup$ @AlexR: good point, but I have often (on many sites, SE and other) wished I could vote independently on content, tone and style between +2 and -2. I see this answer as useful, if in a limited way, so I would give it +1 on content. The mouseover says "this answer is not useful", rather than "... is wrong", which, according to what you say, is inappropriate for meta -- but does that apply to answers offering information rather than concrete proposals? -- I take it no one wants to twist the wrists of the apparently incurious! $\endgroup$ – PJTraill Dec 28 '16 at 19:29

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