I am a long-time user, been on the site for $59$ months, and have a reputation just above $57,000$ on the main site. I have made a fair share of mistakes on the site, both in my answers, as well as in answering duplicates. I have taken some steps to rectify certain issues. I cannot speak for others, but I will talk about the problems I went through, and how I attempted to rectify them and succeeded to some extent. I will speak about personal problems and then about site problems, because I believe the question is: why do high-rep users do this, and I think the site structure contributes to that behaviour, but not as much as the users themselves contribute to it.
Briefly these are:
"I know the answer to this question!"
Flow
Fake competition
Do I have anything else to do?
Need to feel relevant and reduce daily stress.
Problems
I know the answer to this!
I was so quick to share my knowledge, the fact that "I know the answer to this!" and I would jump into answering questions without checking for duplicates, or sometimes even seeing that there was no context to the question and it had a lot of downvotes. While I won't call this a "trait" of a high-rep user,
I think it is something that might actually persist if you become a high-rep user. I give three reasons.
First, because it is what served you well when you were of low reputation and "if it ain't broke, don't fix it".
Second, unfortunately new users are likelier to blindly upvote an answer by a high-rep user than by a low-rep user merely because they think the high-rep user knows what he/she is talking about even if the answer is in actuality short/incomplete/wrong (I mean, he/she has better "reputation"!), so the method works better if you have high-rep.
Finally, if you have higher-rep, you've also got more mathematical knowledge than earlier so you can now answer more questions. This happened with me: it started with real analysis and number theory, and went to probability and functional analysis.
Flaunting : I did this! Sometimes there are clever tricks to solve problems, and you know the trick but other don't. You are very aware that there are duplicates that cover the trick, but instead you want to tell everybody that you know the trick, and know that someone will up vote because the trick is novel to them. Naturally a high-rep user knows more of these tricks, and as I entered a $25,000$ rep mark many of my answers were of this kind. Did I notice this then? Absolutely not. High-rep users could flaunt both knowledge and their reputation with an answer.
Flow
As a mathematician, and having interacted with people from other creative arts, I find the concept of "flow" very nice. It's like, there's that one day when your thinking is at an all-time high, you're pulling off all the right arguments and you just want to keep going, and not break off. You see one question, give an answer that you think is great, and think today might be the day to go on a run, and answer more questions so you can keep the momentum going. I am not sure how many people connect with this, but as an undergraduate student, that flow was addictive. I want to say this with a strong tone: This is a selfish use of the site. I don't know how many people agree with me here.
I want to differentiate this from the previous section: constantly feeling the need to telling others that you know something (as in the previous section), is different from constantly testing yourself out on site questions just because you want to keep a feel-good factor and momentum going.
This could be more of a factor with high-rep users, because for high-rep users, it is easier to give correct answers and keep going because they have far more arguments in their armoury to recall and reuse.
Fake Competition
I was quite competitive as a child, to the extent that I would invent fake competitors
My school crush was one of them, and she never knew about it!
to improve myself in a certain field. It worked with mathematics, to be honest. When I got on the site, I saw other people who started out with me, realized that we would be competing for questions because our levels of knowledge were the same. So, I was the first to new users, and wanted to get ahead of them! I was therefore answering terrible questions. This sense of fake competition did not go until I near $40,000$ in terms of reputation.
One would presume this to be a problem even with high-rep users, because even if the "fake-competitors" disappear, the sense of competitiveness has not gone away, and then some placebo will be invented to compete with: I set myself reputation benchmarks that I had to achieve at any cost, and I would sometimes stay up late at night getting to these thresholds. It is even worse during the holidays!
Basically, feeling the need to get ahead of imaginary blocks, just catering to the competitive side of you, is a problem if it means you are entertaining poor questions.
Do I have anything else to do?
This one sounds odd, but sometimes I feasted on questions because I had nothing to do! I felt restless, and wanted to answer questions. But I don't want something too heavy, so I looked for easy questions and answered them because I wanted to do something. I would spend literally hours staring at the "unanswered page", refresh, read the first new question, answer it if I can, and repeat. Reading answers made me restless, I wanted to think, but not stretch myself too much.
This would happen to me when I could not sleep sometimes in the night. I would get on the site and answer some of the questions to calm my mind, and then see if I could get some sleep. My thinking would be scrambled at this time, so I would even get answers wrong, but just wanted a platform to think.
Could a lot of high-rep users be using MSE for this purpose? I cannot speak for them, but I would like to think that this restlessness doesn't go away when you have a higher reputation, it worsens because a bad habit has formed, and is more difficult to break when your reputation is higher, because you've been on the habit that much longer!
I need to feel relevant and reduce stress
The need to feel relevant is very important, and can have a very damaging effect. For example, if I was a guide and I had a student, then I could impede my student's research if I constantly felt the need to tell him what to do because I had done it, and my opinion on the issue mattered. Furthermore, in conversations I get a kick out of having something the others don't have, and feel left out if I don't have anything to contribute. The need to constantly be contributive, relevant, making yourself known, can distort the benefit of contribution! Also, the need to be contributive increases after an incident of "non-contributiveness", like a bad exam and/or a conversation where you felt left out. You don't want to be left out, and so keep answering questions to remind people "I'm there, I'm relevant, I matter". This happened so much with me! To reduce stress that often arose from feeling irrelevant in a situation, I would just come and answer a few questions on the site! Also, I felt that if I don't answer questions across a long period, people would forget who I am, and that was a problem to me that I could prevent by answering these easy questions.
That is for the problems that I faced. I imagine these are common to other high-rep users as well, and that's why we are all kind of feasting on the queue of terrible questions.
What problems does the site have that facilitate this behaviour of high-rep users? Reputation is itself a double-edged sword, in the sense that if earned correctly it does reflect which user is truly more reputed, but if earned in a dubious manner it completely misconstrues a user's true contribution to the site. Maybe questions by new users for certain elementary tags should have an upper rep threshold for answering? Maybe high-rep users answering poor questions should be penalized more heavily? Maybe the search should improve? I don't know, but I think this is more of a problem with the way people think, and that has to change by communicating with them.
I go over how I rectified my situation little by little. But I think the site can do some things in this regard. I am kind of scattering suggestions over the place, though.
How I attempted to rectify my situation
Here is the list of steps I took to improve my contribution to the site.
Recognize the problem, visit meta
Any problem is at its worst when I don't even know it is there, or worse, don't wish to recognize it. How many high-rep users are truly aware that PSQs are a problem? I am sure many are. How many are aware but still go for answering it? That is also a big proportion, me included as well.
I started visiting meta only after crossing $30,000$. I read up all the basics of the site once again, started reading the discussions among the moderators and other users, and starting seeing the bigger picture. This motivated me to change.
Can we then educate high-rep users more? At least give them a sense that they are more responsible for the working of the site, and that their actions are more far-reaching than that of a new user? Remember, a new user that comes to the site is first seeing an answer by one of these users, so they are the people to learn from.
Finding things to do
I found a nice hobby, the piano, and found a few other things to do, like puzzling and sport. This made me feel far more fulfilled outside of the site, and I found an improvement in sleep patterns as well. This meant I was more focused while answering questions, and actually wrote better answers to more deserving questions!
I actually changed my music playlist as well, and started to listen to older, romantic, slow-moving Hindi and Tamil songs. These are so calming, and a small change can bring great reward occasionally!
Challenge yourself differently, look at the bountied questions
The bountied questions are likelier to be more novel, of better quality, but most importantly come with a chance for you to stretch yourself out of a mathematical comfort zone. I recently answered a question on symmetric convex bodies, and I had so much fun! High-rep users should look to widen their mathematical repertoire by answering such questions that make them "uncomfortable”: I mean, every research problem is solved by reaching into the abscesses and recovering the hidden gems, but if you want to be stuck in a mathematical quagmire of answering PSQs, then it just is not rewarding anymore, an absolute lose-lose situation! I would say, cross the seven seas looking for questions that make you uncomfortable. Sometimes, there's a good user who just posts brilliant question after brilliant question. I followed (not stalked, I reserve stalking for crushes) a few users in this manner, and it helped broaden my view.
How can the site help? Maybe it can suggest high-rep users who have answered too many questions in one field, to explore questions in an unrelated field? (Periodic) Rep-caps for certain tags, a suggested feed of highly voted questions from "rare" tags for all high-rep users, these come to mind as well. I had to come up with these on a daily basis for myself.
We are all in this, nobody is competing
Different users need different ways to understand this, but: nobody is competing with you, and this is a community where everybody has come together to learn mathematics. I am not sure the site can do much, but people need to see if they are using the site as it should be used. Sure, there can be minor conflicts of interest, but I basically want to contribute to this site by writing good answers, asking good questions, eliminating the bad apples, and in return having good conversations, learning new things. If this site is not for you, then please do not use it! Not an MSE thing, but there are sites where our PSQ entertainers, for all their answers here, can actually earn money by answering stock standard questions from students. If you want to be instructional and only use the site for selfish purposes, then such a site better serves you.
It is possible that some high-rep users have reached where they are, without really realizing that they had this mindset! I realized it, and as I mentioned earlier, recognizing this problem was halfway to solving it. I knew I was not competing with anyone: this not only reduced stress from fake competition, but it also meant I wasn't in a hurry to answer questions.
Feel the question a person has, and it is not wrong to comment or look for duplicates!
How many times have I attempted to answer a question without really answering it? There are many occasions where I have not sought to clarify the situation and just answered the question, or just answered something unrelated to the actual question.
Look, it is true that all we know of someone's question is what he/she types in that box. Is that true? Sometimes, the problem is deeper or symptomatic of a particular kind of issue.
Please comment before answering. Two reasons: you get to gauge the OP's interest in his/her question and his/her level of expertise, and also get to clarify if the question is correct, if it is part of an ongoing competition or exam, if there is an XY issue, or anything relevant that could change both your and the OP's perspective of the question. This is a contribution not measured by reputation, but I would say is just as important. I don't know how this can be rewarded. Some suggestions are having badges for people who make "constructive" comments. For example, comments leading to an edit, upvoted comments, comments pointing out duplicates or linking to other MSE questions? Maybe the OP of a question can mark a comment as useful and that could be worth a little bit of reputation. I know these can be gamed, but that is the other extreme: at the moment these are worth nothing, maybe they should be.
Commenting is a very constructive way of behaving on the site. I think high-rep users should be encouraged to comment more often, pass their opinion on questions, link papers and related questions in the comments. Any rule encouraging this is nice! I now comment far more often.
Then there is duplication. A lot of people have written that it is difficult to find duplicates. There are many things that you can do to find duplicates:
Use the search bar for specific tags or keywords, the inbuilt duplicate finder in the close dialog box, or search engines like Google.
Use Approach0, the search engine for math terms, which works for Stack exchange. For example, searching for $x^n+y^n = z^n$ will get you everything you want for Fermat's last theorem.
Check on site lists like here, here (this is the best one, which gets you related questions as well).
It is true that the search is not without its faults. But then again, if you have the slightest hint that the question is a duplicate but you can't find it, comment about the question, tell the OP to look for similar questions, or just don't participate. How do you get such a hint? I don't know, but if you've seen the exercise in a common book, say one of the real analysis books or linear algebra books standardly used (please ask the OP to mention the source if you don't know it), then it is likely to be a duplicate. Recent competition questions are not likely to be duplicates, especially if they are from more obscure competitions.
EDIT : As Nate points out below, a lot of high-rep, or long time users feel that they are so completely acquainted with the site and the usual flow of questions that come in, that they can judge from looking at a question whether it is instantly a duplicate or not. Furthermore, if there is a doubt, then they prefer to err on the side of incaution, for reasons such as laziness, "it is fun to write answers", and last but not least the reputation.
I agree with this sentiment, because I have seen that sometimes newer members of the site are actually more inclined to moderate the site, help out in terms of editing/closing poor questions, assist fellow new users in getting to know the site's working and ethos (showing more patience in this process, I might add), and last but not the least writing some really nice answers that have not been rehashed.
I think the points I have already made are beneficial with regards to this particular habit : if long-time users are made aware of the fact that this behavior is unacceptable (which they would if they visited meta more often!) then they should wisen up. Another suggestion of mine is to have weekly rewards, via reputation, badges or whatever, to users who do a lot of good work on the site, like closing questions, making "useful" comments (refer to earlier paragraph on how comments can be rewarded), spotting duplicates , making useful edits, helping new users (can be acknowledged by having new users ratify you in some way). Broadcast their names across the site, create a merit list that is easier to access which contains their names. Anything to inform users that if a contribution of this nature is also appreciated!
There are still some things as a high rep user that I could be doing better: maybe I could be closing more questions, maybe I could be cutting out some sloppiness from my answering of certain questions.
But I wanted to cover in this answer:
Why high rep users might answer bad questions, both from such a user's perspective and from the site perspective.
What people can do about that behaviour, and what the site can do to curtail it.
