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Sorry, this was most probably asked before in some form, but I haven't managed to find the original.

Let me describe a hypothetical situation related to this question. User $A$ posts a simple homework problem. Another user $B$ with quite respectable reputation (say $>5000$) gives an upvoted, though wrong answer, or correct answer obtained by wrong reasoning. After an exchange of comments, and finally an explicit request for $B$ to delete or correct his answer, nothing happens. Except that $B$ deletes his most glorious comments on the matter.

What should be done? Giving a correct answer doesn't seem to be an option, since most likely the only person who will read an already answered elementary question will be $A$. Should one flag the question or simply let it go down so that $B$ becomes even more respectable or...?

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Giving a correct answer doesn't seem to be an option...

It certainly is an option.

since most likely the only person who will read an already answered elementary question will be A.

You must be reading the already answered elementary question in order to be experiencing this conundrum, right? Moreover leaving a new answer will bump the question, which will almost certainly give it more views.

I think it is an excellent idea to leave your own answer when a question has an accepted answer that, after some careful thought and possibly dialogue with the accepted answerer, you believe to be incorrect. I encourage you to do so.

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Well, you can downvote any answer. You should do it if the answer is wrong.

Do not, however, flag the answer. It will be declined with the template

flags should not be used to indicate technical inaccuracies, or an altogether wrong answer

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There is no way to force another user to delete their answer. There are only three things you can do:

  • Politely point out the error in a comment

  • Downvote the answer

  • Leave your own, correct answer

These do not always leave a satisfying result, but there is nothing else that can be done within the structure that the website provides.

This sort of situation is one reason it is important to read answers carefully before voting, even if the person who wrote the answer has a high reputation.

At the same time, it is important to remember that, as an abstract principle, "correctness" of a natural-language proof can be interpreted differently by different readers. One person may think that a proof is just fine, while another thinks it has an enormous gap or begs the question. In most cases these disagreements can be worked out in comments, but not always.

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    $\begingroup$ Perhaps one should mention that the 20K+ "trusted users" have the ability to vote to delete answers with a negative score. $\endgroup$ – user642796 May 2 '13 at 13:35
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    $\begingroup$ @ArthurFischer: I would, however, not argue in favour of doing that to delete "wrong" answers. If the answer already has a negative score and has comments indicating that the answer is wrong, it may be more instructive to readers to leave the answer up instead of deleting it. $\endgroup$ – Willie Wong May 2 '13 at 13:50
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What you can do.

If you see that an answer is wrong, there are a number of things you can do:

  • Leave a Comment: Depending on the age of the answer, it is likely that the answerer will see the comment, and will be able to incorporate your suggestions or corrections into their answer. If the answer is fatally flawed, they may decide to delete the answer themselves (I've done this a few times when others have pointed out that I am being an idiot).

  • Downvote: The essential idea of the SE model is that good content will be upvoted and rise to the top, while poor content will be downvoted and disappear from view. Votes are used to facilitate this sorting. If an answer is wrong, then it is low-quality content, and ought to be downvoted.

  • Post a New Answer: If an answer is wrong, and no one has posted a correct answer, then you should feel free to do so yourself. When doing this, it is entirely appropriate to point out the flaws in the other answer, though you should not be using an answer to reply directly to another user---use comments for this. Make sure that your new answer actually addresses the original question, and not just the previous answer.

  • Use Standard Flags: You can flag an incorrect answer as "low quality" or "not an answer". Note, however, that not everyone in the community necessarily agrees that outright wrong answers should be deleted, so your flag may be declined (either following community review, or by a moderator). There has been some discussion of this in the past:

  • Comment in CURED: The CURED (close, undelete, reopen, edit, delete) chatroom is intended to be a place where posts (questions or answers) which need special attention can be discussed and handled. If the previous options have failed to have a satisfactory result, discussion in CURED may be beneficial.

What you shouldn't do.

There are also several things which you might be tempted to do, but which you really should not:

  • Flag the Answer for Moderator Attention: Don't use a custom flag. The "not an answer" and "low quality" flags send the answer into a review queue, where it will be reviewed by the community. Using a custom flag will send the answer into the moderators' review queue, where it will have to be handled by a diamond moderator. Generally speaking, moderators do not unilaterally delete wrong answers, and so it is highly likely that a custom flag will be declined.

  • Edit the Answer: Edits are meant to correct minor grammatical or typographical errors. Edits should not be used to change the meaning or intent of a post. Lord_Farin has provided a succinct set of criteria for determining whether or not an answer edit is appropriate:

    Accept when:

    • The mistake is likely due to a typo or some other obviously inadvertent error and is corrected by the edit.

    In all other cases, e.g.:

    • The wrong (version of a) definition was applied;
    • The wrong implication is proved;
    • A theorem's hypotheses were not fulfilled,

    my stance is that the edit should be rejected because the meaning of the post is changed in such a way that only the author could do this.

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I think another possibility is just to edit the answer provided so that it is correct. I'm new to the community so I'm not certain about the etiquette of edits, but it seems like this is a good example of why the option exists. I have edited a couple answers already to have them be more clear or correct (in the case of an actual inaccuracy).

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    $\begingroup$ If the original author of the answer disagrees about whether it is correct, editing the answer against their wishes would be impolite. This has happened in the past; see meta.math.stackexchange.com/questions/793/… $\endgroup$ – Carl Mummert May 2 '13 at 13:40
  • $\begingroup$ Thanks for the link. Good to know that my edits have been accepted and meet the conditions for good editing presented in that question. I suppose if a question contains a serious content error there is not much else to do other than down vote. $\endgroup$ – agktmte May 2 '13 at 13:52
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    $\begingroup$ @agktmte. ... and leave a comment indicating why the answer is wrong. (When doing so, it is not at all necessary to say that you downvoted; this bit of information is of no actual use to anyone). $\endgroup$ – 75064 May 2 '13 at 14:01

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