What makes an answer a duplicate answer?
An answer is a duplicate if it is posted significantly later than the other answer (we should decide how many minutes later) and contributes nothing new that is not already stated in the earlier answer.
Example answer 1 (not a real answer):
It is always a bad idea to copy in examinations. Especially bad to collaborate with a friend in this illegal action. If you get caught then you can be suspended for upto 3 years or even dismissed from the course. It can affect your future! f you get away with it, you will end up lacking confidence in the subject because you know you passed only because of that small folded sheet of paper concealed in your boot. Moreover it will always be an interpersonal embarrassment between you and the friend who helped you copy your way to a passing result.
Answer 2 was written 35 minutes later:
Don't copy! With or without a friend. I still avoid the friend who helped me copy and pass History in high school. I was almost caught copying but I ate the piece of paper and escaped. One of my classmate got caught copying and got suspended forever. He was too decent and didn't get me caught as well. He left school and got into bad company, later joined a bikers gang. I got lucky but still feel I am not good enough in History. Now I wish I had tried to pass the paper without copying. My children think copying in exams is ok but I say: Don't do it, it's just not worth it!
Make up your own mind whether it's a duplicate.
What do we do with answers that aren't really a duplicate, just very similar?
Keep both. The member who wrote the later answer might be encouraged in comments to edit the answer to make it significantly different in content, scope or details from the earlier answer.
What do we do with duplicate answers?
Answers can only be deleted as 'very low quality' or 'rude and abusive', I think. Is it even possible to delete an answer as off topic or a duplicate, except indirectly by somehow calling it a very low quality post? Moderators please enlighten me in comments.
As far as I know we are not (yet) closing answers but only questions as an exact duplicate of an earlier post. So the best we could do at present is find a way to clearly and prominently inform the people writing answers to read all previous answers and be sure not to go write an answer that basically has nothing to add to an earlier answer.
With such an information system in place, we could then consider developing community consensus on deleting answers flagged as duplicate. As you have pointed out elsewhere, that will not make the answer disappear irretrievably @Tinkeringbell. It is similar to a 'put on hold' question: if OP is willing and able to edit their answer to give fresh and original advice then the answer is 'no longer a duplicate' and can be reopened (I mean undeleted.)
However, as noted in @Catija's excellent answer on the earlier meta question,
We also need to remember that answers posted shortly after the question is asked, within a short period of time (15-20 minutes) are often written without knowledge of each other. As someone who's spent upwards of an hour on an answer, I think we should be even more forgiving with similar answers posted within a short period of time as it's even more likely that there's no ill intent.
And I completely agree with the most crucial point made by @Catija's answer:
I think we need to be considerate of the difference between two answers having the same exact solution and answers that have the same "TL;DR" but make granular - and sometimes valuable points. IPS is all about subtle differences. (...) unless the posts are very short and have no differences between them at all, it's unlikely that we will have any truly identical answers.