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For ordinary users (so not focusing on the problems of what subsequent moderator action is appropriate, etc.) I am interested in understanding how to best handle cases of plagiarism, when noticed by a user.

Below are some guiding questions for the discussion, but I'm sure they don't cover everything, so please share whatever you feel is relevant, if you want to. I do not know my own answers to these questions.

  • Is it ideal to only flag the post(s) to inform moderators of the problem, and leave no public trace of the notice?
  • Is there value in making the general audience aware, e.g., through commenting on the plagiarized post(s), possibly bumping the thread(s) (say by editing in the source(s)), or pointing out clear cases of plagiarism on meta?
  • If there is value in making it public, is it outweighed by the drawbacks (e.g., the public drama that should not be the point of our activity here)?
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    $\begingroup$ A somewhat related question, but more on the question of official policy and moderator action: Proposal for a plagiarism policy. $\endgroup$ – Jonas Meyer Feb 22 '13 at 15:30
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    $\begingroup$ Do you mean copy/pasting from external sources (which happens all the time, and to which most people here seem apathetic)? Or are you referring more to plagiarism between users, e.g. this nonsense? $\endgroup$ – Douglas S. Stones Feb 22 '13 at 15:45
  • $\begingroup$ @Douglas: Both. I suppose there are different levels, and it is personal for users exactly when they are triggered to assign the term "plagiarism". I often see questions where the source is withheld, even when asked directly, and this annoys me, but that may be more of a gray area than dishonestly claiming mathematical work as one's own. I hope that useful discussion can occur without having to precisely define for now where the line to most serious plagiarism is crossed. $\endgroup$ – Jonas Meyer Feb 22 '13 at 15:57
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    $\begingroup$ I already don't understand the reasons for the default policy of keeping everything private. Without understanding the benefits of that overall policy, I can't evaluate its benefits as it applies to this particular situation. $\endgroup$ – MJD Feb 22 '13 at 16:03
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    $\begingroup$ @MJD: I don't know all the reasons, but I think that public drama can be harmful. On the other hand, I suppose that informing the general users of certain problems may be helpful. I don't know what general policy there should be to balance the two. I am guessing there is great diversity of opinion. $\endgroup$ – Jonas Meyer Feb 22 '13 at 16:08
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    $\begingroup$ Asking a question copied verbatim from some source is not plagiarism. In any case, I don’t care what the source of a question is, unless it’s an on-going contest or examination, and don’t really understand why anyone else does, either. (Yes, there are some exceptions, when a specific reference really would be helpful in establishing context, but they are far less common than calls for the source of a question.) $\endgroup$ – Brian M. Scott Feb 22 '13 at 17:51
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    $\begingroup$ As for actual plagiarism, what @Douglas refers to as this nonsense is the only kind that’s been mentioned that I think absolutely needs to be dealt with. (E.g., I don’t approve of answering by copying some source verbatim without credit, but in most cases an equivalent answer could have been provided from many other sources, so no one’s toes are really being badly stepped on.) My preference in those cases would be to flag silently, though I can imagine being sufficiently irked to leave a comment, especially if it happened more than once with the same person. $\endgroup$ – Brian M. Scott Feb 22 '13 at 17:57
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    $\begingroup$ @Brian There have been problems with plagiarism of external content. One extreme case in Fall 2010 was a user who amassed huge rep by posting a very large number of unattributed contest questions and answers, often implying that he devised some of the ingenious answers. Eventually, after doing this with a couple easily recognized gems, e.g. Zagier's celebrated one sentence proof on primes that are sums of squares, the ruse was uncovered (much is deleted by now). This incident is what sparked Pete's Proposal for a plagiarism policy. $\endgroup$ – Math Gems Feb 22 '13 at 19:00
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    $\begingroup$ @MathGems: I consider such problems special cases, to be handled as they arise. I don’t think that they require special policies, and I’ve enough of an anarchistic streak to prefer keeping formal policies to a minimum. $\endgroup$ – Brian M. Scott Feb 22 '13 at 19:09
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    $\begingroup$ @MJD: This is a small community. If you mark someone as a plagiarist it will be very hard if not impossible to shake this image off. Even changing names, or registering new accounts can only hold you off for so long... much like some people are clearly past users and many people recognize their style easily. This is more the case because having a meta thread "Is X plagiarizing Y?" is an immediate mark onto X and an immediate victimization of Y. Some debates and arguments are won by whoever makes the first move, even if X does not lose their reputation (not points) entirely, it's still a blow. $\endgroup$ – Asaf Karagila♦ Feb 22 '13 at 20:17
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    $\begingroup$ I should add that at least for me this is more than just a site on the internet. If I were to be [seriously] accused of plagiarism from other users, I will definitely be very very upset about this, and it will most likely disrupt my everyday life for at least a short period of time. $\endgroup$ – Asaf Karagila♦ Feb 22 '13 at 20:21
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    $\begingroup$ @Asaf I really don't thin so. In the case that motivated, I certainly assumed that some user was just a bit too paranoid in an area where answers are relatively easy and much alike. Then came more evidence and I adjusted my expectations. I don't thing with everything documented on meta, we have to worry too much about village rumors. And actually being found out for plagiarizing should hurt ones reputation. $\endgroup$ – Michael Greinecker♦ Feb 22 '13 at 20:33
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    $\begingroup$ @Asaf I think we both tent to agree that the average user doesn't look as often on meta as he or she should. One can be suspended for spiteful downvoting and still run succesfully for mod here. Threads can be deleted, and 10k+ uses should be able to apply some judgement in such situations. I think you are very much an exception in how much you identify MSE- something the rest of us profits from a lot. As to more common real live issues- I think we should be much more careful in accusing those who are easily identifyable in RL. It should definitely not be the first google hit for a name. $\endgroup$ – Michael Greinecker♦ Feb 22 '13 at 20:46
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    $\begingroup$ @gnometorule: I wish you'd stay, but I am not going to force anyone to do anything. Except sets, choice principles and cardinal properties. :-) $\endgroup$ – Asaf Karagila♦ Feb 22 '13 at 22:57
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    $\begingroup$ @Michael: I agree that the average user doesn't care about meta affairs, even if we only average those who stay and actually get involved with the site a bit (in contrast to unregistered users asking and leaving). But it's still a possible outcome. As for me being an exception, I recognize the compliment you are giving me and it is always nice to hear your efforts are being appreciated (I think the 70k rep. was a hint, though :-)). I can't stop thinking how much am I an exception, or maybe I'm not. I've known enough mathematicians to know that I might not be after all. $\endgroup$ – Asaf Karagila♦ Feb 23 '13 at 2:45
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As the author of the post who likely initiated this one, I would like to chip in. Jonas is known for very well-written and thought-out posts. In my reply I will simply list thoughts that come to my mind, which aren't necessarily related to one another:

(1) Privacy policy: It stands to assume that a privacy policy exists to avoid ugly he says-she says fights in public. Plagiarism is rather different. For the most part, this is a community of active, former, future, wannabe, and failed academics; a community in which plagiarism is a very serious offense - or it should be in anyone's eyes. If you plagiarize here, what are you doing/will you do/have you done in academia? Don't complain if you get into the public eye. You should be.

Obviously, there is the counter position, and correct observation, that someone wrongly accused might carry a stigma even if justly exonerated. But in my eyes, the above outweighs this drawback: how often will that happen? Who would make such a mad claim if it isn't 99% certain?

(2) Who is the plagiarizer? If a 135 rep user decides to make a post which consists of having copied one each by BMS and AN, with some MathOverflow thrown in, it strikes me as easily handled and, to an extent, as humorous. If the third highest reputation gainer of the month has a long history of plagiarizing, it strikes me as very worrisome, and worthy of public debate to elicit feedback.

(3) Value of going public: Had this not gone public, it is almost certain that not all cases that are outlined in EN's answer would have become known. The final feedback to my claim of plagiarism is 'not proven as there is some debate.' After I submitted my post containing the sentence "Assume next that it holds for some generic n. You need to show that then it also holds for n+1. As it holds for n, you can assume that", other user user posted 5 minutes after me, with changed indices - but the same bracket missing in the same spot - an addition to his post starting with "Assume next that it holds for some generic k. You need to show that then it also holds for k+1. As it holds for k, you can assume that" (emphasis added). By this standard, there are several German ministers who would still be in office as opposed to enjoying salary increases from now being in industry. I tried to avoid pointing to this as I have already stepped on too many toes, but I can only scratch my head. One of my favorite users here keeps chipping in implying that nothing has been proven, while rather clearly defending other user, for reasons I honestly do not understand.

So it is good that the other cases which might not have come public, actually did, because had I only flagged my post, and had my claim only been evaluated based on its own merits, it would apparently have been declined (this is assuming that moderators would not have found the other cases, which obviously is not clear - in fact, I am sure some would have been found. Still.).

(4) Burden on the moderators: The particular case was clearly eased by allowing others to do their own digging, and chipping in. The moderators do a great, and burdensome job - and probably will reply that they don't mind, that this is due process, and they volunteered to it, which is true. But relying on a community to chip in, in this particular case, reduces some of their burden, and speeds the process up. Edit/addendum: It is also easier for other users who might have experienced it first-hand to remember such cases because what happened might be buried in edit history (at least one of the cases reported was only visible, I believe, when unrolling such history), which would mean that a moderator, obviously, not originally involved would not only have to compare posts, but posts as edited over time.

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    $\begingroup$ (+1) Very well thought and written. I'm completely on that side. $\endgroup$ – Gottfried Helms Feb 22 '13 at 18:35
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    $\begingroup$ +1: Just adding the point that if a closer examination reveals that someone is/was wrongly accused, it will be reported here in meta, and not just in the local equivalent of a small print notice on page 37 of the newspaper that originally posted the false accusation on the front page. $\endgroup$ – Jyrki Lahtonen Feb 22 '13 at 20:00
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    $\begingroup$ @gnometorule Excellently written. $\endgroup$ – user14082 Feb 23 '13 at 8:10
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I would prefer that plagiarism were handled by the moderators, since I think it's best to minimize the amount of drama and mudslinging here on meta.

However, this requires that the moderators do handle plagiarism allegations with diligence and seriousness. That the moderators were aware of amWhy's plagiarism almost a month ago and joked about it/did nothing, and more recently seemed dismissive of gnome's complaint, leaves me with less confidence on these points than I would like.

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    $\begingroup$ Just wow to your second paragraph. It might help explain the 'humorous' treatment of the case by some of great influence here. This site, of all places, shouldn't reflect the power abuse rampant by those in charge in the world of politics, and I can only wonder who other user is in real life, and how (s)he handles her personal relationships there. To react with arrogance...I simply don't know what to say. $\endgroup$ – gnometorule Feb 22 '13 at 19:11
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    $\begingroup$ To be fair, at the time of the first linked instance, there didn't seem to be much evidence of plagiarism. For all robjohn knew at the time, it was just a fluke. As more examples were dug up, the moderator team responded more seriously. I can't comment on the second linked instance. $\endgroup$ – BW. Feb 22 '13 at 20:30
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    $\begingroup$ I fully agree with Ben. I personally would be sceptical about someone accusing one of the highest ranking users from copy-pasting arguments in elementary mathemtics too. $\endgroup$ – Michael Greinecker♦ Feb 22 '13 at 20:36
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    $\begingroup$ For what it's worth, I can verify that the moderators are handling this case with the diligence it deserves right now. Sometimes it takes a while to put together definitive proof and it can't hurt to be certain and avoid wrongly accusing someone. (Disclaimer: I'm a community manager at Stack Exchange and we can see and review moderators' actions.) $\endgroup$ – Adam Lear♦ Feb 22 '13 at 23:20
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    $\begingroup$ My comment to AmWhy was in response to a deleted post about which Guillermo commented to AmWhy: "you almost copied my comment". AmWhy removed the post and Guillermo seemed okay. I commented on Guillermo's post, but it did not seem to warrant any further attention. I apologize if my comment to AmWhy seems inappropriate. I would not have made light of the situation had I thought plagiarism was involved. $\endgroup$ – robjohn♦ Feb 22 '13 at 23:48
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    $\begingroup$ Considering the in depth analysis I did of the incident between gnometorule and AmWhy, I don't think I was in any way dismissive of the situation. Perhaps it was inappropriate for me to discuss the possible outcome in chat since warnings and suspensions are to be discussed among the moderators and communicated privately via email. In no way do we take plagiarism lightly. However, often it is hard to prove that it has occurred. $\endgroup$ – robjohn♦ Feb 22 '13 at 23:48
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Moderator Erik Naslund remarked here:

I would like to thank each user who pointed out and flagged these different threads, as discovering such plagiarism would be nearly impossible without your help.

That could only happen because the original plagiarism was made public. In particular, I was aware of one instance but was willing to write it off as a weird fluke until I saw gnometorule's report about the same user.

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To answer to Jonas' question.

How is plagiarism best handled by non-moderators?

$(1)$ Flag the offending post for moderator attention. Try to provide as many details as possible in your flag.

$(2)$ Leave a comment which indicates the source, and explain that it should be cited.

$(3)$ Depending on the scenario, the user should contact the moderators directly providing a full account using a private chat room.

The recent example of plagiarism was an extreme case, one that has never been seen before on Math Stack Exchange. The details were not so clear until gnometorule created this meta thread, it seemed unlikely that a high reputation user would be copying answers to elementary questions, but in hindsight the flags were incorrectly dismissed.

$(4)$ If you feel it is necessary, create a meta thread and start a discussion. While there are some drawbacks to making everything public, I believe that in such cases this is far outweighed by the benefits of resolving the issue. As was the case with the recent incidents, this eventually led to the resolution of the problem.

Formal policy against plagiarism:

Pete L. Clark proposed a formal policy against plagiarism, and the following system of responses on the part of the community and the moderators:

a) First a user gets a warning that their behavior constitutes plagiarism. A warning should make reference to at least one specific post, with the idea that there should probably have been other instances of problematic behavior that could be pointed to as well.

After a user has been warned, they should be contacted by a moderator to ensure that they have received and understood the warning. I'm not sure whether any formal response from them is necessary.

b) If a user continues to plagiarize after being warned, they next get a suspension of at least one week in duration. Moreover, at this time the user must engage in off-site communication with at least one moderator and display a willingness to stop their problematic behavior.

c) If a user continues to plagiarize after being suspended, they next get expelled from the site. Moderators will try to ensure that this same person does not reincarnate under another username, at least not in an obvious way.

My amendment to this policy is in part (b). If a user continues to plagiarize after receiving an official warning, they will be suspended for at least 30 days.

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    $\begingroup$ I think that in order to provide sufficient evidence and details the flagging process is not sufficient. Perhaps the user should request the moderators to contact them through email, chat or moderator message where a longer and full account of the details can be given. $\endgroup$ – Asaf Karagila♦ Feb 22 '13 at 22:55
  • $\begingroup$ @AsafKaragila: Agreed. I will add this to the list. $\endgroup$ – Eric Naslund Feb 22 '13 at 22:57
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    $\begingroup$ I would suggest chat over email because it allows for a record to be kept somewhere on the site that others (other moderators, employees, etc.) can review later if needed. Moderators can also annotate users even if there isn't sufficient evidence to warrant action, but keeping notes for future reference would be handy. $\endgroup$ – Adam Lear♦ Feb 22 '13 at 23:10
  • $\begingroup$ @AnnaLear: For that very reason, when I added Asaf's suggestion to the list, I only put the suggestion regarding giving the details through the chat. $\endgroup$ – Eric Naslund Feb 22 '13 at 23:29
  • $\begingroup$ I still feel that a moderator message might be a good suggestion; but I suppose Anna knows the system's inner works much much better than me. $\endgroup$ – Asaf Karagila♦ Feb 22 '13 at 23:31
  • $\begingroup$ @AsafKaragila Moderator messages are usually reserved to address serious behavioral issues, and suspensions. $\endgroup$ – Eric Naslund Feb 22 '13 at 23:34
  • $\begingroup$ @AsafKaragila There's no way for a user to send a private message to a moderator outside of flagging something. Every private mod message thread has to be initiated by a moderator and, as Eric notes, these are reserved for infractions. (We on the community team also get copied on every mod message sent.) $\endgroup$ – Adam Lear♦ Feb 22 '13 at 23:36
  • $\begingroup$ @Anna, Eric: I suspected as much, and indeed the fact that the community team is automatically CC'd (or rather BCC'd) is more than enough to keep this in the chatrooms. $\endgroup$ – Asaf Karagila♦ Feb 22 '13 at 23:37
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    $\begingroup$ How do you define plagiarism for the purposes of this answer, and, in particular, item (1)? Judging from @Brian M. Scott's comment above, we have quite different opinions of what constitutes plagiarism. $\endgroup$ – Douglas S. Stones Feb 23 '13 at 12:58
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    $\begingroup$ @Douglas: Points (1)-(4) don’t actually require a definition: users will flag/comment/post to meta according to their respective definitions, and the moderators will have to sort it out. The formal policy, on the other hand, does require some sort of definition, but I see no need for and strongly dislike the idea of a formal policy. $\endgroup$ – Brian M. Scott Feb 23 '13 at 14:41
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Without knowing about the existence of this question, 12 hours ago I was at the point of directly coping a part of this answer of Jonas Meyer:

Ahlfors's complex analysis text has a footnote on page 21 of the 2nd edition, 1966:

Modern students are well aware that $f$ stands for the function and $f(z)$ for a value of the function. However, analysts are traditionally minded and continue to speak of "the function $f(z)$."

I was thinking that this would be an excellent addition to my answer in this question. Normally, I would have done this anytime, as it wouldn't have felt like stealing. But I was aware of the post from gnometorule, so I didn't do this. I was scared that people would see this as plagiarism.

Today I wake up and I see that, out of all people, Jonas Meyer asks a question about plagiarism. To be honest, I feel like most people here are judging far to harshly on copying a part of someone else answer. I mean 90% of the answers here are just some rewriting of already existent answers (in books or in the internet) anyway.

As math is such an exact being, many times I feel like rephrasing an answer so that it isn't direclty copied as something almost redundant. Should I have rephrased this text from Jonas Meyer answer: "Ahlfors's complex analysis text has a footnote on page 21 of the 2nd edition, 1966", so that it isn't directly copied?

If an answer is some creative unique representation of math, I think it would be very disrespectfull to directly copy this answer in your answer without refering to the author, but otherwise I don't see why people would judge direct copying of math as a serious crime.

I see MSE as a place where people help each other out with math problems, and I'm really glad that this place exist. But if I read the posts here I get the impression that some think of MSE as a place where people can officially publish their math papers.

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    $\begingroup$ In that situation I would say something like ‘According to this answer, Ahlfors’s complex analysis text ...’ or possibly ‘According to this answer by Jonas Meyer, Ahlfors’s complex analysis text ...’. If I had the book, however, I would probably just quote from the book, even if it was Jonas’s answer that reminded me of the possibility. I would not simply quote the answer with no reference to if of any kind. I wouldn’t beat up on someone who did, but I don’t really approve, either. $\endgroup$ – Brian M. Scott Feb 23 '13 at 14:28
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    $\begingroup$ I mean 90% of the answers here are just some rewriting of already existent answers (in books or in the internet) anyway. There’s considerable truth in this, but I object a bit to just: rewriting can add considerable explanatory value. $\endgroup$ – Brian M. Scott Feb 23 '13 at 14:37
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    $\begingroup$ The problem lies in the highly subjective value-judgment of "creative unique representation of math". A student may be rightly proud of (re)discovering some old chestnut, so may be offended by someone copying it. But an expert might say, as Noether often did, "it's already in Dedekind!", and may be glad to see others help propagate such gems. Generally, one doesn't know where along this spectrum the author lies, so it is better to exercise (some) caution (but not so much that it is painful, e.g some things like standard exercises are widely copied without attribution). $\endgroup$ – Math Gems Feb 23 '13 at 18:07
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    $\begingroup$ In the case at hand, it were 2 answers to the same question, with other user copying my solution (verbatim, indices changed which alludes to a feeble attempt of obscuring, and some words at the end erased), as an addition into her solution 5 mins after I post. Or go to her answer on complex numbers recently, where even after JM had pointed to two quotes that had been copied verbatim, the first revision had "on which I will elaborate after" - the 'personal elaboration' being another verbatim quote later found to be from MathOverflow. So it's a bit different from your case. $\endgroup$ – gnometorule Feb 23 '13 at 19:39

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