Should we vote to delete wrong answers?

Question

It is not difficult to notice that sometimes an answer is deleted (by users other than the OP)¹ simply on the grounds that it is considered incorrect by the users who voted to delete. (Probably if you follow meta, you have seen some questions sparked by such deletions. If you have access to moderator tools you might find some such deletions there - although I do not see an easy way to distinguish between deleted answer and deleted questions there, so this might be not easy. Or you might have even seen discussion of such deletions in chat.)

EDIT: Based on some comments (some of them now deleted) it seems that I did not make this sufficiently clear, so I will stress once again that I am asking about deleting answers by users other than the OP.¹ Self-deletions probably deserve to be discussed separately and I believe there already have been a few such discussions.²

On the other hand, on meta.SE I read that wrong answers should actually be downvoted, not deleted. At least in the case that the answer is actually an attempt to answer the question, but it is incorrect. (As opposed to "not an answer".) Some relevant posts from the main meta: Why shouldn't I delete wrong answers?, What can be done with a blatantly wrong answer to a popular question? and When should I delete an answer? To make the reference to the network-wide policy bit more specific I will add an exact quote from FAQ item: How does deleting work? What can cause a post to be deleted, and what does that actually mean? What are the criteria for deletion? from the part "What are the criteria for deletion?"

For answers, any post that is not an answer (should be a comment, doesn't answer the question, etc.) should be deleted. Answers that are wrong or that dispense poor advice should be downvoted, not deleted.

Of course, there is wide range of what could the phrase "wrong answer" mean. Obviously, if an answer is posted which has altogether nothing to do with the question, such answer should be deleted. (The most extreme cases are spam posts, but there might be even answer which seems closer to an answer and is at least partially related to the question, but the main purpose of the answer is to promote answerer's blog or answerer's own results on theories.)

Here I mean an answer which clearly is an attempt to answer the question. It might be possibly wrong. But the OP decided not to delete the answer or simply abandoned it. (For example, the OP might disagree with the assessment of other users and still think that the answer is correct. Or the OP thinks that even if the answer is incorrect it is still useful.) In situations like this, is it ok if other users vote to delete this answer? Or is a better simply to downvote the answer (and possibly comment) but without delete vote?

Clearly, there is wide range of opinions on this. Some users argue that downvotes and comments are not strong enough indication that something is incorrect. (Especially in cases where downvotes are compensated by pity upvotes or upvotes by users who did not spot the mistake or do not have sufficient understanding of the topic.) On the other hand, sometimes there might be disagreement whether or not an answer is actually wrong. (So, for example, an answer might be deleted by a few users who consider it incorrect. And the fact that there are some other users who consider the answer satisfactory, does not prevent deleting the answer. At most, if the answer has some upvotes, this makes deletion a bit more difficult since the answer has to reach negative score first.)

Clearly, there were some related discussions in the past. For example, Wrong answer is not corrected/deleted or Deleting Wrong Answers in "Low Quality" Queue. (Maybe also this one; although the discussion there seems to be mainly about questions: Are we too trigger-happy about deleting (relatively) new posts?) But probably it is ok to have a new question discussion about this. After all, the site evolves. And, additionally, some activity on meta in the past few months seems to indicate that this is now a topic which several users have on mind.

Since from past discussions seems that users of this site has very differing opinions on this, it would probably naive to expect that some consensus is reached. But even if we at least see clearly formulated positions of some factions and if each side at least has opportunity to hear arguments for different viewpoints, I suppose this might be useful.

TL:DR; Suppose that an answer is not blatantly out of place but it is genuine attempt to answer the question - although perhaps incorrect. Is it ok to cast delete votes on such answer? Or should incorrectness be pointed out merely by comments and downvotes?

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¹Users which have at least 20k reputation can vote to delete answers. See Privileges - Trusted User for some basic info and FAQ on deletion for more details. An answer can be also removed if it is deleted together with a question, users with 10k+ rep can delete questions. But here I am asking specifically about voting to delete single answer, not about deleting question together with all answers.

²Here are some posts related to self-deleting incorrect answers: Protocol for deleting wrong answers., Deleting a downvoted answer?.

Answer 1

In my opinion, the author of incorrect answers should, when an error is pointed out, delete their answer unless (or until) it is amended. If the author feels that the error is of value to the site, it is acceptable to edit the post to include a prominent notice right at the top that it is erroneous, and explain where the error is, correctly, and preferably explain how to fix or circumvent the error.

I even go so far as to say that authors that sincerely attempt to answer the question will never leave an incorrect answer lying around without fixing or deleting it, once it has been pointed out. Hence when the error has been pointed out and yet the author refuses to fix it, then I am totally in favour of deleting it, since sincerity is indeed lacking.

Answer 2

Sometimes I have posted a wrong answer. (Hard to believe, I know.) But it seemed to me that the wrong method might be considered by others, so I left the wrong answer, and added a boldface This answer is wrong at the top, and an explanation of why it is wrong.

You may consider doing that when your wrong answer may still be instructive to others. But it could happen---and has happened to me---that (even though marked This answer is wrong) you still get a few more downvotes for it.

Answer 3

It is obvious from my reputation (as for the time I'm writing this) that there is still time before I'll be able to vote for deleting, but I still want to say my opinion because I do think it is an important matter.

I think that the function of voting for deletion should be used only on very unique cases:

1- the answer is not related at all(less relevant to this discussion).

2- the answer(wrong or not) is using methods that was pointed out by the OP of the question as something he/she is not looking for. I think that the most common case is when asking a question in limits without L'hospital's​ rule. In my opinion those kind of answer should be deleted because they serve no purpose for the question.

3- the answer is wrong and the mistake doesn't help. For example if someone misunderstood the question he is answering.

Apart from those cases I think that mistakes can be very important and should never be deleted. But I'm not saying they should be leaved.

Each mistake is from one of 4 main types of mistakes:

1- answering using blunt wrong information, for example using a lemma that wasn't proven.

In this case this question should be downvote and commented about the mistake and giving the OP to decide what to do(delete/edit)

2- misusing something, for example using a theorem before all of the conditions to use it are indeed there.

In this case I think that downvotes are unnecessary, you should add a comment pointing it out or edit it to be better. Because even if this, say, theorem can't be used at all in that question pointing out the mistake will make people recognize the mistake and will help them in the future. If such a mistake will be downvoted I think a lot of people that can learn from that will just ignore it.

3- some algebra mistake

This should be just edit but whomever spotting it

4- a "mistake" in how can we use something. For example if I am saying that $\lim\limits_{x\to0}\frac{\sin x}x=1$ because $\sin\theta=\theta$ for small angles.

This case is the most complicated, I think that this case should be judged by each person. If you are think this is a serious mistake downvote and comment it, If you think it is a small detail just comment

I think that none of those mistakes should be deleted because people can learn from those things a lot.

The last thing I want to talk about I'd about answers that one simply don't understand, in those cases one should ask for explanation or just ignore it.