Is it right to delete a downvoted answer of one's own? I have only done this once (I actually got the "Peer pressure" badge from that), but I am afraid that this is not allowed. I do have an accepted answer on MSE with -6 votes, but it cannot be deleted because it is accepted (which is good). My question:
Is it allowed to delete a downvoted answer that you posted for any reason, whether it be gaining back reputation, or simply embarassment?
Thanks in advance
Deleting posts is a natural part of using a Stack Exchange site. Not everything once written should be preserved, lest we want to create the Library of Babel. Of course, if a post can be saved with an edit, you should do that. But sometimes editing isn't worth it: e.g., what's written is entirely wrong, and the correct points to be made are already made in other answers. Users are given the ability to delete posts for a reason.
More specifically:
If you feel that the answer is unsatisfying, and feel that it contains wrong information, then deleting it is fine. Two points about that (in addition to those made in the other answer) are:
If you delete an answer and post essentially the same answer (up to a minor modification), you are likely to get downvoted even more than before. It is unacceptable to delete something because of downvotes, and hope that posting it again will not accumulate new downvotes.
Sometimes it is positive to have mistakes visible. In that case you might want to edit your answer that it is a mistake, point out why, and perhaps make it a CW if you don't want to gain or lose further reputation on that. We learn by falling down and making mistakes, so it can't be all bad to see mistakes from time to time.
The best course of action in your case is to convince the original asker that your answer is incorrect. And ask him/her to unaccept your answer.
Once the user does that, you can vote to delete the answer yourself.
If the user is unresponsive, and if you have a preponderance of evidence that your answer is in fact incorrect (e.g. numerous downvotes, many comments from third party users pointing out its incorrectness), you can flag the answer and ask a moderator to delete it for you. (We prefer not to base moderator actions on our evaluations of factual correctness of an answer; hence we ask that some evidence that the "community is on your side" be satisfied before we heed a request to delete an accepted answer.)
Yes, it's a natural part of looking after your own work but also looking after the site as a repository for good quality information. For me, reasons for this include:
Most frequently, I started writing an answer and then realized it was garbage. Sometimes someone points this out to me after I post it, but mostly I realize myself. And there's absolutely nothing wrong with deleting in response to a slew of downvotes (assuming those downvotes are justified). If the answer's wrong but still useful in some way I will sometimes leave it up with an appropriate comment.
There's another answer which is a superset / much better than mine, and mine adds nothing (especially if my answer has no votes).
General tidying up the site. For example I recently posted an answer to a question which was subsequently closed. I deleted my answer and added it as a comment to the question instead, as my answer wasn't that great anyway and higher rep users had decided it shouldn't be answered.
Several times recently I've also temporarily deleted answers, when I've realized that what I first wrote was wrong, before revising and undeleting.
