Downvoting unnecessarily complicated/irrelevant answers?

Question

Quite often I see simple questions asked and people offering answers that are clearly not going to make any sense to the OP because of the gap between the knowledge assumed by the answer, and the knowledge the OP has (as inferred from the question). Here is a case in point. This isn't an answer to the question, really. It's just someone showing off what they know that is vaguely related to the question.

Is this an acceptable practice, or should we discourage this kind of irrelevant answer by downvoting?

Please note: if you want to downvote the question, leave a comment explaining why. Disagreeing with what I suggest is not a reason to downvote the question. Even if you think my suggestion is not the right way to go, you should agree that it's worth asking the question...

Answer 1

Question is not only for asker — maybe someone else (e.g. someone looking for an answer for more or less the same question — but with different background) will find the answer interesting. So I think, this kind of answers is OK.

Upd.: especially since asking duplicate questions are not allowed.

Answer 2

If you don't understand the answer, you are not in a position to judge whether it is "unnecessarily" complicated. Mathematicians think about even simple problems in a very different way from non-mathematicians and they will naturally give answers that reflect this. As Grigory M says, this could be quite valuable to a student who stumbles upon the answer in the future and finds a sophisticated perspective that teaches him something.

If, on the other hand, the answer contains genuinely irrelevant information and nothing else, then of course you should downvote it.

Answer 3

@Seamus: I think you are undercutting your point by the particular example you cite. Certainly Arturo Magidin's answer is an actual answer to your question. It begins:

"'Permutation group' usually refers to a group that is acting (faithfully) on a set; this includes the symmetric groups (which are the groups of all permutations of the set), but also every subgroup of a symmetric group."

That's the answer to your main question. He then goes on to provide additional insight into what's the point of saying "permutation group" when every group is a permutation group. (In summary, yes, every group is isomorphic as an abstract group to a permutation group, but the same group can be realized as a permutation group in multiple ways, some of which tell you a lot about the structure of the group itself, and some of which seem not to.) This is much more than just vaguely related to the question, and Arturo is not "showing off"; he is a research mathematician in the subject of algebra who is taking time out to share some of his insight.

This is an illustration of Qiaochu's point: the OP is not necessarily in a good place to evaluate all the answers to the question. However, the system allows for multiple answers and allows you to choose the one which you like best, which then gets displayed at the top, even if it is not the most popular answer in terms of upvotes minus downvotes.

Were you actually satisfied by the answer you accepted? If so, the system worked the way it should. If not, you should unaccept the answer and clarify what more you are looking for. Note also that although some people are going to pitch answers at a higher level and/or riff on things of interest to them, others will look carefully for clues as to the OP's background and use this information to craft an answer at the right level. (I think both of these practices are valuable, and I have done both myself in answering questions.) You can certainly help out the latter people by including as much relevant information about yourself, your general math background, and your math background specific to this question. For instance, based on your reaction to Arturo's question I am guessing that you are a beginner in abstract algebra, but your question did not convey that.