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Here's the situation I ran into:

I posted an answer to Maximum $C$ such that every shape in $\Bbb R^2$ with area $<C$ can be placed to avoid $\Bbb Z^2$ and it garnered a few upvotes before I realized that it was utterly wrong and not really salvageable (the nature of the problem is to give a shape, and the shape I gave was invalid).

I deleted it, and came up with a new answer. The new answer followed basically the same proof idea as the old answer, but was for quite a different shape. At this point I didn't know if it was appropriate for me to add a new answer, or to (significantly) edit my previous answer and undelete it. I ended up doing the latter.

Which is preferred: Adding a new answer or significantly editing your older wrong answer?

It wouldn't matter much except that there were already votes on the wrong answer, which would be invalidated by leaving the answer deleted (and I don't know if the votes should be invalidated or not). If the votes had been down votes, then it would make sense to post a new answer because presumably the down votes would be in response to incorrectness which would not (necessarily) apply to the new result.

Here is a related discussion, but it is different from this one since it just concerns adding information: http://meta.math.stackexchange.com/questions/10843/when-should-you-add-another-answer-instead-of-adding-to-your-previous-answer

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There should be some continuity to the content of a post; an edit should be an edit, not a new post in the same box.

Thus, if the second answer is completely different from the first I would go for a new post. If there are only major changes, but there is still some continuity an edit seems appropriate.

It is not completely clear to me what was the case for your post. But you said the basic idea was the same, so I think any edit was still reasonable.

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    $\begingroup$ Peter wrote: "The new answer followed basically the same proof idea as the old answer, but was for quite a different shape." So I agree that an edit, essentially correcting a (fatal) flaw, would be the best approach. $\endgroup$ – hardmath Jun 11 '15 at 19:59

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