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At one point I wrote a fairly detailed explanation of why equivalence relations on a set and partitions of that set are essentially the same thing. The issue came up in a new question again. The new question is not a duplicate of the old one, so closure as a duplicate is not appropriate. (The original question was specifically about the left cosets of a group, and the new question is more general, just complete bafflement about equivalence relations: What exacly are equivalence classes.)

It was tempting to copy most of my previous answer, which I was happy with, into a new answer to the new question. In the past I have not usually done this, and instead have left a comment pointing to the old answer. That is what I did this time. My feeling is that such cases are good opportunities to let other people write their own answers. On the other hand, I think my old answer is pretty good, and might be helpful if reposted. Although the idea of posting the same answer twice makes me uncomfortable, I am not sure why, and I have not been able to identify any specific moral or ethical problem with it.

I am interested to hear what other people in the community think about this.

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    $\begingroup$ I think it's up to you. $\endgroup$ – Gerry Myerson Apr 24 '14 at 14:03
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    $\begingroup$ I think it is fine. I would add a parenthetical note indicating that most of the answer is a repost of something you wrote for a different question, and include a link. $\endgroup$ – Andrés E. Caicedo Apr 24 '14 at 14:19
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    $\begingroup$ You could post it as a community wiki, with a link back to the original question. This makes it look like you aren't gaming for reputation (and if you post a link then you will probably get a few upvotes there anyway). $\endgroup$ – user1729 Apr 24 '14 at 17:03
  • $\begingroup$ (Although I notice that the original is already a CW, so it a moot point for this case. However, in general, I think a CW is best.) $\endgroup$ – user1729 Apr 24 '14 at 17:06
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    $\begingroup$ Circumstances in which the activity of discussing mathematics could lead to moral or ethical problems are very limited, involving unusual applications like nuclear weapons, optimization of computer viruses, or questions that are proxies for such. It is very interesting that the people who think that ethical problems appear with, e.g., answering homework questions ("please help with [exact copy of exercise] before Wednesday!") do not take the strange appearance of an ethical issue in such an innocuous activity for what it is: a reductio ad absurdum of their moral assumptions about homework. $\endgroup$ – zyx Apr 24 '14 at 23:29
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    $\begingroup$ @zyx: Surely the OP's doubts were about the ethics of the reputation game. As are many other "political" disagreements in meta actually. Including the HW issues. I believe the way they distort the rep game is one of the underlying gripes people have. Not everybody will confess it publicly (but I do). That game is a big driving force here, so any built in or perceived unfairness in the game will come to the surface. $\endgroup$ – Jyrki Lahtonen Apr 25 '14 at 7:47
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    $\begingroup$ Surely the OP's doubts were about the ethics of the reputation game. // To avoid any misunderstanding: the comment on strange non-inferences related to homework had nothing to do with the OP. The use of the words "ethical" and "moral" in the answer led to one observation, which was then applied to a different situation related to the homework discussions on meta. @JyrkiLahtonen $\endgroup$ – zyx Apr 25 '14 at 13:20
  • $\begingroup$ This post is (to some extent) related and also contains a few links to discussion on the main meta: Should identical answers on questions which are abstract duplicates of each other be allowed? $\endgroup$ – Martin Sleziak Apr 15 '18 at 3:42
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Ethically speaking, I think it's perfectly fine to repost your own answer to a second question. It's certainly better than answering with a rushed, inferior version of the old answer, or feeling forced to paraphrase a copy of your old answer.

A better long-term solution might be to build an indexed list of blog-like in-depth treatments to commonly-asked topics, and point people there. (We have the beginnings of something like this with our "generalization of common questions" list).

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    $\begingroup$ I disagree with this answer. It looks like reputation gaming. EDIT: Sorry, is reputation gaming. Why else would you not put it as a community wiki than to get extra reputation? $\endgroup$ – user1729 Apr 27 '14 at 21:19
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    $\begingroup$ IMO, I don't see how getting reputation for your work, while you're giving a user an excellent answer to their question, is "gaming" anything. I also oppose the use of Community Wiki for anything not involving either "community" or "wiki", but of course I wouldn't mind if someone felt uncomfortable receiving extra reputation and checked the box. $\endgroup$ – user7530 Apr 27 '14 at 21:44
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Duplication of content is a problem, even regardless of ethical and moral considerations (and they exist). What if your original answer contains a minor flaw that you overlooked, and someone notices it and correct it? Now there are two slightly different versions of the same answer on the site, one with a flaw and one without. You also deprive the people finding the new or the old question from learning about a different point of view about the same thing, assuming the question weren't already duplicates of each other.

At the very least there should be links, preferably in both directions, indicating that the answer was copied. A better option in most cases, IMO, would be to make a whole new answer, explaining why the old answer solves the question and then link to it. Something like this:

By theorem XYZ, we can see that your hypothesis A is equivalent to some other hypothesis B, and so by this answer your object satisfies property W which implies what you want to prove for such and such reason.

Of course, if you apply this reasoning, you will sometimes be left with an answer that looks like "This older answer solves your problem." In this case, the new question is actually a duplicate of the old one and should be closed, instead of answered.

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Several prominent members of the community expressed support for this behavior, and nobody made any serious argument against it, so I conclude that it is all right to do it.

On thing I thought of after I asked the question: When reposting an answer, it may be tempting to paste the text in without re-reading it. But such re-reading is important. Questions do differ, and the old answer might be missing discussion of some point that is important in new context but not in the original, or vice versa. It ill-serves the community to let such copy-pasted answers appear without editing. So one must take care that the answer is really well-suited to its new home, and perhaps do a bit of tailoring to make sure it fits.

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One should be careful not to commit self-plagiarism. Although it's not too big of a deal (based on part of Willie Wong's answer here), I believe some do frown on it, and it's often best to avoid it (it's a big no no in academia for obvious reasons). I would therefore stick to the advice which a few others have given, such as setting your answer to community wiki so that you don't double dip on reputation and making the appropriate citations and links to your previous answer, stating clearly that it is a duplicate answer. These steps aren't necessary as far as I know and I believe there is no site rule saying otherwise (I could be wrong), however I would say these steps should be made out of good faith.

There is also the practical question of the site software automatically flagging an answer as a duplicate, which I have seen happen in the past. If you do post an identical (or possibly near-identical?) answer to a different question, there is a high chance that the answer will be added to the review queue for 10k+ rep users.

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  • $\begingroup$ Does anyone know if making an answer community wiki removes such a duplicate from the review queue? $\endgroup$ – Dan Rust Apr 25 '14 at 20:39
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    $\begingroup$ As the wiki article points out, "self-plagiarism" is controversial even within academia, where it is frowned upon primarily for logistical reasons (it is extremely frustrating, as an editor or reviewer, to spend a lot of time on a submission only to have the authors retract at the last minute and publish somewhere "better" instead). I personal don't think self-plagiarism poses any ethical concern in the stack overflow environment, but reasonable people might disagree. $\endgroup$ – user7530 Apr 27 '14 at 21:49
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    $\begingroup$ @user7530 Why does the author retract? Why do not both journals publish the paper? Presumably because there is contrary to what you imply no doubt that one should not publish the same thing twice (in any case not without indicating this is what one is doing). $\endgroup$ – quid Feb 9 '15 at 14:23
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Who said there was anything wrong with "reputation gaming"? Come on!!! This site is about two things (primarily): 1) To help each other and 2) Have fun.

The points are both functional and also about fun. Its not like the points are going to make a difference on whether or not you get that promotion or find a post-doc.... at the end of the day, this is just a game where everything is made up and the points don't matter. In fact what should keep you from posting $someone$ else's work on the site?! Its not as if anything $is$ really yours to begin with anyway. Mathematics works because we build on each other, and the answers here aren't going to result in anything so even citation-less answers of others ultimately isn't really a big deal.

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  • $\begingroup$ I realize that my answer is quite different than everyone else's but after all this ISN'T some real academic program... it's just Math Stack Exchange. $\endgroup$ – Squirtle Apr 28 '14 at 22:01
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    $\begingroup$ ... which is a complex academic program? $\endgroup$ – GEdgar Feb 9 '15 at 13:52
  • $\begingroup$ I don't think this really addresses the question; it is not necessarily more helpful to post a duplicate answer than to post a link in the comments - and, I don't know about you, but neither action sounds like a whole lot of fun. $\endgroup$ – Milo Brandt Feb 9 '15 at 14:41

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