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First of all, I need to say that I do not intend to start a controversial topic challenging the community. I'm trying to find a solution and understand the nature of MSE better to see whether it's the place I think it was or not.

In recent weeks, I have seen many questions that are so easy that can be answered by any average undergraduate student (sometimes even highschool students) taking the course in the first or the second week upvoted too many times by the community. I don't want to point fingers at any specific post, but most of these questions showed that the OP had overlooked the most basic of definitions or they did not bother to contemplate for a minute to find counter-examples to really easy and obvious problems.

I find it completely okay that people ask easy questions. After all, I ask silly questions all the time and people should never be discouraged to ask their questions, no matter how easy the question is. What I find strange is that a pattern exists in some of these questions: a user with high reputation (usually +100K) gives an answer to the question and then suddenly the question shows up in Hot Network Questions. The OP receives tens of upvotes for asking a low quality question that adds literally nothing to the website (and probably had been asked in other forms, worded differently, tens of times before) and the people who answered it receive tens of upvotes for an answer that their only effort was to type it.

The problem becomes serious when somebody, genuinely in need of help from the experts on the website, asks a really good question about a relatively advanced topic that shows real research effort, but not the kind of research that could be asked on mathoverflow. The first problem is that this kind of questions never get upvoted more than two or three times, if they get upvoted at all. Also, they're not viewed many times either, even with bounties, because many people do not have the necessary knowledge and expertise to understand and answer them. Then many users, in particular the professional mathematicians on this website, avoid answering these questions because even if you write an amazing answer, there's a high chance that your answer won't get upvoted more than twice.

This means that people who want to use MSE for advancing and widening their mathematical knowledge are left out and nobody wants to help them. We say we are not a homework website, and if you hover your mouse over the upvote button, you see "This question shows research effort; it is useful and clear", but what happens in reality is not very in line with what is said. Also, people who ask questions that are advanced undergrad level or graduate level can't go to mathoverflow because they will say that their question is not research level. So, they will get no help from stackexchange at all.

What do you think we should do about all this? How can we encourage mathematicians active on MSE to use their powers for good?

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    $\begingroup$ Some people are motivated by reputation. Opportunity to gain reputation is increased with an increased "footprint" of solutions. A quick way to open up a new bit of footprint is to answer easy questions and not put a whole lot of work into it. Therefore, it is logical for people motivated by reputation to engage in this behavior. So the answer to your title question seems to be "yes, of course" but I think based on the body of your post you are asking something more nuanced. $\endgroup$ – rschwieb Feb 18 at 20:29
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    $\begingroup$ In order to prevent people from answering low quality questions or adding low quality answers, you'd have to appeal to them to stop caring about reputation, I suppose. That sounds hard to do in general. Maybe the best we can hope for is leading by example, voting judiciously, and keeping the resulting answers at least correct. $\endgroup$ – rschwieb Feb 18 at 20:31
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    $\begingroup$ It absolutely does, and there are many high rep users here who got that way because they farm the exact same calculus or algebra questions over and over again, and who have realized that they can trade their ethics for a little green number. I am losing faith that there is a good solution to this within the SE framework. Gamification is too effective. $\endgroup$ – user296602 Feb 18 at 21:48
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    $\begingroup$ As a follow-up, I don't think reputation directly encourages LQ questions. It encourages LQ answers, which in turn encourages LQ questions. $\endgroup$ – user296602 Feb 18 at 21:51
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    $\begingroup$ The reputation system serves to reward activity. This seems to be an overall positive thing without taking into account the quality of questions and answers. Is the reputation system responsible for low quality questions and easy answers? I too don't think it is responsible for low quality questions. However, it is responsible for the activity low quality questions receive. Whether the accepted answer is of high quality or not (in my opinion) has to do with the patience the OP has. If a low quality answer is accepted, then I am less inclined to provide a higher quality answer. $\endgroup$ – Alberto Takase Feb 18 at 22:32
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    $\begingroup$ I would like to add that we are facing two problems now: 1- Too many low quality questions receive too much attention, 2- Good questions are not well-received because answering them is not rewarded properly and few people understand them. I believe the second problem is more serious. There's a solution to this problem: we should have a system where contributions in subjects that have fewer experts/watchers/readers are valued more than questions in precalculus algebra or calculus. However, I do not know if MSE has the flexibility to adopt such a system. $\endgroup$ – stressed out Feb 19 at 9:08
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    $\begingroup$ As you said if people want to ask a serious question, they usually need to use bounties to draw reasonable attention at the questions. But this costs a lot reputation and usually you don't get it back by upvotes on these questions. Consequently, if you have a serious question you need to "farm" reputation first in order to be able to start a bounty. Thus I think you can't (too much) blame people for answering LQ questions with LQ answers - it might be a necessity for them to get their own questions answered. $\endgroup$ – user526015 Feb 19 at 10:04
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    $\begingroup$ @James I'm not really blaming people for answering low quality questions. As I said, any question regardless of how elementary it is deserves to be answered. What I am trying to criticize peacefully is that low quality questions receive tens of upvotes and people answering them receive sometimes over 50 upvotes for a trivial answer. On the other hand, real 'good questions' are ignored because they don't receive enough upvotes and experts stay away from them due to low activity. I once offered a bounty on one of my questions. After 1 year and 2 months, it has been viewed only 58 times so far! $\endgroup$ – stressed out Feb 19 at 10:11
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    $\begingroup$ @stressedout this wasn't supposed to criticise your post. I just wanted to add an additional line giving a possible explanation why so many people answer LQ questions regardless of a similar question with answer that one could refer to. Unfortunately, I see the very same problem and I'm glad you make a point here on meta! $\endgroup$ – user526015 Feb 19 at 10:17
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    $\begingroup$ A cuurent example: math.stackexchange.com/questions/3116417/… $\endgroup$ – YuiTo Cheng Feb 19 at 10:44
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    $\begingroup$ @ParamanandSingh I strongly disagree with downvoting correct answers even for low quality questions. The real purpose of the voting system is to show whether a user, be it the OP or another viewer, can trust an answer given to the question. If we downvote a correct answer, the user might think that the answer is incorrect which is not true. The only reason to downvote an answer should be that the answer is incorrect or incomplete. I know that isn't your point of view, I'm just criticizing the view shared by crude people. $\endgroup$ – stressed out Feb 21 at 13:48
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    $\begingroup$ @stressedout I disagree with that assessment. We are to upvote answers that are useful, and downvote answers that are not useful. A correct answer is not necessarily useful if it, in a sense, justifies the presence of a substandard question. There is a lot of disagreement, and you are welcome to criticize my stance, but a lot of users no longer equate correct and useful. For example, if a high rep users posts a straightforward application of Carmichael function number 471 to settle an elementary question about congruences, my judgement tells me that such a post is not useful. $\endgroup$ – Jyrki Lahtonen Feb 22 at 10:00
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    $\begingroup$ Having said that, my observations suggest that isolated downvotes don't work as deterrents, the penalty is too small (and the penalty a single user can inflict absolutely must be small). A better disincentivizer is to vote to delete those posts. $\endgroup$ – Jyrki Lahtonen Feb 22 at 10:23
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    $\begingroup$ @JyrkiLahtonen "A correct answer is not necessarily useful if it, in a sense, justifies the presence of a substandard question." I don't like the sound of that. If a low quality question generates answers of some value, then yes, this adds to the value of the question. I don't think it's right to blame the answers for making questions not as worthless as you want them to be. $\endgroup$ – Theo Bendit Feb 23 at 2:25
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    $\begingroup$ @JyrkiLahtonen If the answer is duplicating an answer to a duplicate question, then the answer is not useful. It's not really "justifying" the presence of the question at all. If a useful answer does appear, I do think it makes the question less worthless, and I don't think answers should be judged more harshly because of it. It also troubles me to see you effectively dismiss the argument on the basis of an ad-hominem fallacy. Hitler was a vegetarian, but it doesn't mean we should excuse vegetarianism on a case-by-case basis. $\endgroup$ – Theo Bendit Feb 23 at 5:53
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Mathematics, unlike most other branches of human knowledge and experience, is relatively universal in the sense that everyone has to take some mathematics classes in their academic career. This means that a very large number of people either are currently, or have in the past, worked through the kind of basic algebra and calculus problems that show up here again and again and again. Because of this:

  1. These kinds of questions get asked a lot. Since many people have to work through the problems, there is a large population of students who are ready to ask them. However, these students often haven't engaged with the mathematical community at all (since they are, for example, anthropology majors), hence they don't really understand how to pose a good question. Thus there is a significant portion of the population which seeks to ask questions here, but which doesn't know how to ask. Hence the large number of low-quality questions on basic topics.
  2. There are lots of people who feel qualified to vote on these questions. Because the questions cover basic material to which a large number of people have been exposed, there are a large number of "casual" MSE users who can look at a question, say "Huh... I don't know how to answer that... +1!" The jargon-y educational explanation is that these are questions that are smack dab in the middle of the "zone of proximal development (ZPD)" for a large percentage of the population. The questions are simple enough that a lot of people recognize that they ought to know the tools used to obtain an answer, but they are just hard enough that a good percentage of those users don't know how to actually get that answer. We (i.e. humans in general) often get a warm fuzzy feeling when we see material that hits us in the ZPD, so such questions are more likely to get more views and more upvotes.
  3. There are lots of potential answerers. Because large numbers of people are exposed to elementary mathematics, there is a large pool of potential answerers. This means that elementary questions often get quite a few answers fairly quickly. Moreover, the answers are either going to be exactly what those folk in (2) are expecting (giving them warm-fuzzies and encouraging them to upvote), or the answers are going to have some idea that appears novel (the folk in (2) therefore learn something new, and upvote because of this).

Essentially, there are a large number of people who desire answers regarding "basic" material, there are a large number of MSE readers who can understand and vote on such questions, and there are a large number of MSE users who can provide answers. This means that basic questions (and their answers) can garner a lot of upvotes before falling off of the front page.

As a corollary, the folk that answer such questions can earn a lot of XP... er... reputation fairly quickly. Indeed, there are a fair number of high rep users who have made their "careers" on MSE by answering such low hanging fruit with profound regularity. I would note, however, that I am not asserting that the reputation system encourages this. Rather, I think that the reverse is kind of true: the high reputation earned by such questions (and their answers) indicates that the modal (i.e. most common, average) voter on MSE has only a limited mathematical background. Users engage with—and are rewarded for their engagement with—familiar topics.

On the other hand, more advanced questions are less likely to get attention. The majority of MSE readers are not going to be able to even understand such questions, let alone feel qualified to vote on them, and there are orders of magnitude fewer users who might be qualified to answer such questions. Because of this, more advanced questions can very easily fall off of the front page before they get seen, and are unlikely to ever be highly upvoted. Frankly, I think that this has little to do with the reputation system, and is more a symptom of the fact that basic questions simply dominate the conversation. It is a kind of "denial of service" attack, I suppose.

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    $\begingroup$ I think you have mentioned some of the reasons why the phenomenon exists. However, the purpose of my post is not to study why it exists. We all know why the situation is the way it is and many of these reasons had been mentioned before. The thing is that this phenomenon has a serious side effect: it makes MSE less profitable for people who want to study/understand mathematics. I think that the main audience of MSE should be people who want to study/understand mathematics, not people who just happen to have encountered math some time in their life and they need help with their homework. $\endgroup$ – stressed out Feb 19 at 21:05
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    $\begingroup$ The question in your title is "Does the rep system encourage easy answers and low quality questions?" I answered that question, and elaborated on it: the problem is not the reputation system, but the average user, who lacks the background for deeper questions, but is willing to ask a basic question. The inflated reputation is a side effect of this. Unless you are willing to give 95% of the user base the boot, I don't think that there is much that can be done, other than working hard to prune the crap. $\endgroup$ – Xander Henderson Feb 19 at 21:16
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    $\begingroup$ I believe there are ways of correcting the reputation system. For example, we can divide question tags into three categories: elementary, intermediate, advanced. A question will be in one of these three categories depending on its tags. So, if a question's tags are $(1,1,0,0,0)$ where $0$ denotes no tag, then the average is $1+1/2 = 1$ which means that it's an elementary question. Then we can accordingly modify our reputation system to put more weight on advanced questions than elementary questions, et cetera. But it depends on how flexible stackexchange is. $\endgroup$ – stressed out Feb 19 at 21:20
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    $\begingroup$ @stressedout Your proposal would require a significant investment of time and energy from SE, as it would demand a lot of new code. I wouldn't hold my breath on it. Again, I think that it would be far more productive to actively work to eliminate (close and delete) the crap. $\endgroup$ – Xander Henderson Feb 19 at 21:23
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    $\begingroup$ It's just an unapproved proposal. I have some limited experience in web development as a freelancer. I believe it doesn't need a significant investment. It's possible that it can be done by adding just one new column to their database where they keep the information related to question tags. Of course, it depends on the way they store their data and I know nothing about it. I'm ready to help the development team for free if they want but I'm sure they already have enough top-notch developers. The question is whether they're willing to do something that can make the MSE community better or not. $\endgroup$ – stressed out Feb 19 at 22:23
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    $\begingroup$ @stressedout Why do you think that these new mechanisms will magically ease the maintenance burden? It will quickly be clear which tags reward more reputation, and those tags will be added more often. This might even be defensible if I use cool axiom independence techniques to prove an elementary-set-theory question. And I for sure don't want to be bothered with the meta wars about which tags should be in which category. I'm sorry, but nothing is ever easy, and complex problems demand well-thought solutions. $\endgroup$ – Lord_Farin Feb 19 at 22:50
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    $\begingroup$ @stressedout It has been suggested in the past that there be a kind of "question wizard," which guides askers through the process of asking a good question. My understanding is that something of that kind already exists on SO. Such a wizard is not, technically speaking, that difficult to implement, yet it has taken more than a year to get it up and running, and it is still not widely implemented (i.e. Math SE has no such wizard). What you are proposing is more demanding (since tags have to be weighted; the rep bonuses have to be balanced; &c), which makes it less likely to be implemented. $\endgroup$ – Xander Henderson Feb 19 at 23:07
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    $\begingroup$ Moreover, your proposal is predicated on the belief that reputation drives people to ask and answer low quality questions. I have, in my answer, asserted that this is not the case. Rather, these questions garner votes because they are familiar and accessible. Changing the relative reputation earned by these questions will not (I believe) significantly impact the rate at which they are asked and answered, and the "good stuff" is still going to be drowned out. Again, the solution is to actively work to eliminate the crap. Be more active in the close queue, for example. $\endgroup$ – Xander Henderson Feb 19 at 23:10
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    $\begingroup$ @XanderHenderson I believe that your correct assertion that these questions garner more votes because they are familiar and accessible (which is true and I don't have an objection to this) doe not contradict the fact that some experts prefer to answer this type of questions because they will receive more upvotes. We cannot change how people vote, but we can modify the reputation system or at least discuss possible changes to it in theory. $\endgroup$ – stressed out Feb 19 at 23:53
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    $\begingroup$ I agree with @stressedout. We can't change users' behavior directly, but we can immediately tweak the reputation system. $\endgroup$ – MadnessFor MATH Feb 20 at 1:05
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    $\begingroup$ @stressedout Assigning difficulty levels to questions per tags is an interesting idea, but A) it would lead to tagging wars, B) wouldn't solve the problem with low hanging fruits. Consider the following. A calculus question can be answered by 2000 users, and understood by many more. Granted, most of them are not gonna vote. A highly specialized question in, say, class field theory can only be answered by Matt Emerton, and the answer can be understood by three other users. All of whom are gonna vote (because they follow the tag). What kind of weights would you assign to balance things out? $\endgroup$ – Jyrki Lahtonen Feb 20 at 7:00
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    $\begingroup$ (cont'd) The scale might need to be exponential. And giving a single vote a huge weight would introduce several other problems. Other possibilities for levelling the playing field might work better or not. Introducing an absolute per tag rep cap. After gaining 1000 points answering pre-calculus, that's it. Learn more math or sit there! $\endgroup$ – Jyrki Lahtonen Feb 20 at 7:09
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    $\begingroup$ Or, introduce a per question cap of rep points, and split the points of a single question according to the relative votes on the answers: Sam Sophomore is the first to answer a popular question, quickly reaching the per question cap. Then Jill Junior and Grace the Grad Student come along and give better answers, and the votes given to those begin to eat away Sam's rep. Again, such a system would not level the field because we have ten times more of those easy questions. $\endgroup$ – Jyrki Lahtonen Feb 20 at 7:19
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    $\begingroup$ @JyrkiLahtonen (continued) On the other hand, there are many users who have earned almost half of their reputation by answering questions in precalculus algebra or calculus tags. If we define a reputation cap for these tags, the rules should be applied to everyone, not only the new users. In that case, many of our top users will disagree with this change because they'll lose the reputation they've earned for the time they invested before this law existed. If we apply this law only to new users, then the gap between people who signed up earlier and new users will become even larger. $\endgroup$ – stressed out Feb 20 at 14:05
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    $\begingroup$ @PeterTaylor Is there any place in the world where some kind of mathematics is not part of the standard "academic career"? Not every takes calculus, but I doubt that there is anyone in the world who has attended some kind school and has not been exposed to some kind of mathematics. $\endgroup$ – Xander Henderson Feb 21 at 13:42
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I'm going to invert this a bit.

First, I'll answer your title question: Yes.

...but you probably don't have much of a reason to care, at least for the concerns you seem to be bringing up in the body of your question.

The question isn't "Will lots and lots of people see my question?" but "Will the people who can and want to answer my question well see my question?" I'd argue for high quality questions that would benefit from a "professional mathematician", the answer is generally "yes".

First, I expect "professional mathematicians" to be one of the groups least interested in spending their time giving easy answers to basic questions or caring that much about reputation. It's just boring, and MSE reputation doesn't really translate to really any kind of professional reputation in the math community, certainly not if it is primarily from answering basic questions.

As I've said elsewhere, it doesn't make much sense to view MSE as a single community. Instead, it is fuzzily segmented by tags. I literally never see the vast majority of questions on this site, because I only consider questions that are tagged with topics I'm interested in. StackExchange makes it easy to filter this way. If you tag your question one of the tags I follow, I will see it no matter how many low quality high school algebra questions are being asked. I'm pretty confident I'm not unusual about this with regards to more "advanced" topics. As I've also said elsewhere but I can't find, there's even effectively a tiering of tags for various topics. If you follow the tag, you'll probably get tons of high school/undergrad questions, but if you are a "professional mathematician", you'd be more likely to be following or not . For , it would be things like or .

The upshot is: if you're asking graduate level questions, the people who can and want to answer your questions are going to see them if they are tagged appropriately. You are correct that even excellent answers to narrow, technical questions won't get tons of upvotes. Particularly for the people you are most interested in seeing your question, I don't think that that is that much of a disincentive (if any). (It arguably filters out people who'd produce low effort answers.) It certainly isn't so overwhelming as to make asking the question moot.

I'm not saying that there aren't modifications to the reputation system that might make things better, but I doubt that they would make a big difference, and I don't think high quality, advanced, and answerable questions are routinely failing to receive answers. (At all, let alone due to the reputation system.) Here is one thing that might (or might not) help. Make per-tag reputation (much) more prominent (and probably de-emphasize site-wide reputation).

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    $\begingroup$ I'm not a professional mathematician; I'm just doing my PhD. However, I personally find that my research and my time here helping people stimulate me in slightly different ways. My research feels like a puzzle that I patiently plug away at, enjoying the feeling when two pieces click together. My enjoyment on MSE is derived from the joys of teaching: expressing an initially daunting barrier to mathematics education in a way that makes it seem intuitive, straightforward, and sometimes even obvious. Then, you'll sometimes get to see the penny drop, which is a pleasure in itself. $\endgroup$ – Theo Bendit Feb 20 at 4:48
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    $\begingroup$ My point is, I'm not convinced that a professional mathematician wouldn't enjoy helping people with basic questions, as it is a different joy to research. Although, I'm sure that many of them are burnt out on teaching, which I think is by far the more significant factor in deciding their enjoyment! $\endgroup$ – Theo Bendit Feb 20 at 4:50
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    $\begingroup$ @TheoBendit I agree re teaching, but giving a well thought out and enlightening answer to a basic question is not giving an easy answer. The scenario was giving low effort answers to low quality questions, not thoughtful answers to good but basic questions. That said, for people who use a strategy similar to mine, they will simply never see a high school algebra question, say, in the first place. There's also no shortage of teaching opportunities in more advanced math. $\endgroup$ – Derek Elkins Feb 20 at 6:34
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    $\begingroup$ Fully agree here. +1 I have asked only a few questions here (and none of them being basic algebra / calculus) and the response has been positive on the whole (in terms of getting help). But on the rep side such questions don't give you much. $\endgroup$ – Paramanand Singh Feb 21 at 5:23
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    $\begingroup$ @DerekElkins, depends on the subfield. They don't all have tags which are as well stratified as analysis. $\endgroup$ – Peter Taylor Feb 21 at 9:58

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