If I'm writing a response and when I click post, there are 0 (or, even for argument, 1) answers to a question, and my answer is right (perhaps even the same as another answer), should I delete my answer?
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Noise is bad
If your answers are identical, and you do not have extra information that you could add (to make your answer better) then you are providing NO benefit to the OP, and you are simply adding noise to the question.
This happens a lot on easy questions where people add answers and then leave. The question will end up with four identical answers and one good/great answer. That means that whenever anyone visits the question, they must wade through a lot of redundant space in order to read all the answers.
More answers is not always better, if the more are just more of the same. If there is nothing new to add, then delete your answer.
If your answer is identical to an earlier one: Improve or Delete.
Something that came out of TheTXI defending his own post in a comment. If you post a duplicate answer, you are essentially stealing votes. All of us here recognize the phenomenon where someone will basically copy/paste your answer and then begin to get upvotes while your answer does not.
I don't really have an explanation as to why this happens, and typically it is not due to malicious intent, but the purpose of the site is allow the best answer to bubble to the top. But if you add a duplicate answer, then you are splitting the vote.
I have always looked at it like this: If you are within half a minute (30 seconds) then no. If your answer is different in a way than the earlier answer, even more so no.
Just because someone was correct first does not necessarily mean that their answer is better. You could easily go in and edit your answer to provide more information and then you could start getting voted ahead.
If we all deleted our answers after the first technically correct one came in, we would probably be doing a big disservice to the OP.
devinb writes, "Noise is bad" - this should be your guiding principle when writing for SO.
Atwood has speculated that readers who are truly interested in a question will read every answer posted... if this is true, then by leaving answers that are effectively duplicates you're wasting the time of every interested reader who follows.
I would go so far as to suggest that even if you do add something new in your answer, you should still consider removing it if you see another answer posted, before or after your own, that covers more of the topic or is better written than your own answer. You can always take the unique portion of your answer and edit it into the better answer, or request that the author does so himself via a comment. Alternately, remove all duplicate information from your post, cite and link to the other answer, and follow with your additional information.
Again: fewer, better answers means less wasted time for those who eventually read them looking for help.
I'd say it's up to you.
I tend to delete if my answer turns out to be virtually identical to another one that came in whilst I was typing.
Other answers that are basically the same I've left and then gone back and deleted later, but I've never systematic about this. That's meant that occasionally I've gained one or two up-votes days (or even weeks) later. So clearly someone saw something in my answer.
It happened to me once (^_^). I arrived late, but posted a superior answer. Unfortunately, the community didn't responded as well as I expected, and basically a concurrently placed answer got a way more upvotes, than mine. Besides this, a small argument wars began on my answer's comments. At this point I decided, I delete my answer - there was an equally good answer available and upvoted - and mine had 6 votes - just enough for a Disciplined Badge!
I usually delete my answer if an almost identical one was posted a few seconds earlier. There are a few users who will downvote answers they consider to be "duplicates" even if there is nothing really wrong with your answer.
By leaving your answer, you are accomplishing a few things.
First, you are providing an alternative wording. There's no problem with that at all. In fact, the variations in wording might make the difference between someone getting something and learning and them still having problems.
Second, by having a variety of wording, there are more possible searches that can be brought to a page. That should make it easier for someone using a search engine to find a page on an SO site that has their question and a number of answers.
Third, your wording might help an answerer realize they were vague in one aspect and edit their post, creating a new and better answer.