So I had an answer to this question (actually I answered it on this question before Menachem(?) found the duplicate at which point I also voted to close as duplicate) deleted because it is a duplicate to this (better, more inclusive and sourced) answer. ברוך שכוונתי וכו', but what is the policy here? Are duplicate answers subject to deletion? Where is that described?
If an answer was obviously created in good faith, it's a shame to waste the author's time by removing it. Good-faith answers can reiterate one another to some extent, especially if they're created at nearly the same time. The best one can rise to the top.
Answers that lend nothing new to questions that have long been answered should be judiciously pruned because they become noise. They're little more than "Hey, that worked for me too" in most cases. It's just someone trying to get some points to unlock some of the more basic privileges, at least in most cases, and review does a great job of spotting them.
There is another class, the all encompassing answer that ties together five different answers to a question in a coherent, fluid way. Each answer on its own was useful, but more or less a fragment. When someone ties them all together nicely, well - that's useful stuff to keep around provided they give credit where it's due.
Answers that are legitimately created as duplicates, such as at the same time, or to different questions that end up getting merged, or to expand on an existing answer, should be allowed to stand.
Only an answer which is unjustifiably duplicate - in that it adds nothing to an existing answer and the author knew or should have known about the previous answer, should be subject to deletion at moderator discretion.
For precident I would point to Stack Overflow, which (although I haven't found the signal-to-noise ratio there worth participating in for a while it certainly used to) have many duplicate answers due to simultaneous answers, and they are all left alone.