Does the reputation system encourage easy answers and low quality questions?

Question

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?

Answer 1

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.

Answer 2

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 calculus 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 real-analysis or differential-geometry not calculus. For algebra-precalculus, it would be things like abstract-algebra or commutative-algebra.

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).