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This question is anonymous for obvious reasons.

I referee what feels like a decent number of papers (though I don't know how many is normal!), and I try to take it seriously. Sometimes, based on something I explicitly said or something implicit in my review, the journal rejects the submitted paper. Usually this seems to be because the editor feels that the paper isn't up to the journal's standards.

In an event that has proven less rare than I would like, I am sometimes asked - by a different editor and journal entirely - to review the same paper again. My record is currently three such rotations.

Usually I try to beg off, because I feel like the author deserves to get a new referee who is less biased and might bring new insight to their review. What I've found in practice is that editors tend to persist, and solicit my opinion more informally. I understand this, because I know that referees are hard to find, and so I've usually done so. The editor usually will say that they will seek out an additional referee, though I rarely hear the final story. In some instances I have gotten the impression, for reasons that I don't want to get into, that an author is starting to feel persecuted due to repeated rejections by prestigious journals.

What is the best policy on requests to repeat a refereeing job?

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Community wiki? – HJRW Feb 21 '11 at 19:08
I am surprised that this comment has not been made yet: you could be proactive and suggest other reviewers with the necessary expertise (possibly clearing this with them first!). Don't forget that editors may not have an encyclopedic knowledge of the who's who in you field, so they'll keep sending you papers simply because you may be one of the few people they know who has the necessary expertise. In particular, pass it on to younger researchers, it's good for their career. – Thierry Zell Feb 21 '11 at 20:06
@Thierry: in what way do you think refereeing is good for young researchers' career? – Igor Rivin Feb 21 '11 at 20:49
@Igor: it's not the refereeing itself (though that's not entirely useless), but the fact that you would be actually recommending that person's knowledge and work. I'm thinking that, early on, any opportunity to be a blip on someone's radar can only help. – Thierry Zell Feb 21 '11 at 21:18
When rejecting a paper that you feel is publishable, but belongs in a different journal, why not suggest some journals that you feel the paper would be appropriate for? If the author follows your advice, and you get the paper back from an appropriate journal, you can suggest acceptance. – Dan Ramras Feb 21 '11 at 23:49

I am answering this anonymously, also for obvious reasons. As a referee, I get quite annoyed when, after having recommended rejection for a paper, and given several detailed reasons for the rejection, the same paper comes back to me from a different journal with no changes at all. In other words, the authors didn't even try to address my objections. In this case, I have absolutely no qualms about rejecting it all over again. On the other hand, if the authors genuinely tried to answer your objections, and you still think it is not acceptable in the new journal, maybe you should ask the editor to send it to a different referee.

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Well, I've been on both ends of this I guess, but I would tend to strongly agree with this sentiment. The exception would be when a referee gives a comment like "This paper is boring"-- this is a subjective comment, and in such a situation, it does seem ethically correct to hand over to another referee. (And to be honest that you are giving a subjective comment!) – Matthew Daws Feb 21 '11 at 19:51
If the author has resubmitted the paper without significant change, I would send the editor my original report with a note explaining what has happened. The editor can then choose to use your report, or commission a new one if s/he feels that would be fairer. Note that you are not rejecting the paper in any case - the editor decides whether to reject or accept on the basis of all available information. – Chris Godsil Feb 21 '11 at 20:02
@no name: By the way, "stylistics mistakes" here is a stylistic mistake ;-) I agree that such things (in moderation) shouldn't count toward rejection, but should if possible be corrected to improve readability of a paper. Those of us who grew up with English have to appreciate the difficulty others have in writing for journals that publish primarily in English. – Jim Humphreys Feb 21 '11 at 20:07
In my experience this problem arises when an author has a paper rejected without opportunity of rebuttal. Perhaps when a paper is rejected for mathematical errors concerning a result which would be deserving of publication if correct, the author, if he disagrees, might be given a chance to demonstrate that there is in fact no error. If he has a chance to defend his position, but without success, it might reduce repeated submission of the same flaws. If the referee has rejected it based on actual counterexamples, he should have no reservations about rejecting it unchanged again. – roy smith Feb 21 '11 at 20:53
Besides mathematical and stylistic reasons, papers also get rejected because of unimportance. I once sent a paper to a very good journal and got two referee reports. One said the paper was very good, the other said that everything was correct but the results were not important, the editors decided to reject it. I sent it out again unchanged to a comparable journal and it was accepted. In this circumstance, I see nothing wrong with doing so -- I wasn't going to prove better theorems at that point, and one of the referees thought it was good enough. – David Speyer Feb 22 '11 at 2:27

My personal feeling is that not making the author wait for a second referee to write a report is doing them an enormous favor, even if the paper gets rejected. If you aren't going to write the paper a good enough report to get the paper published, most probably whoever else would referee it instead won't either, and they will take a lot longer.

I have to admit, I also feel like you're not respecting the time of the anonymous person who will have to referee the paper instead of you. Peer review takes up a lot of mathematicians time; it seems like just making the problem worse to create unnecessary duplication.

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Presumably, whichever field this is, you are an expert in it, and the editors respect you as such. So, if you hate the paper, and think it should not be published, I don't see the downside to telling this to all editors who ask. If you don't hate the paper, but think it is not quite Annals-worthy, you can just say in your review "I don't think this paper is suitable for Annals of Math, but I think it would be well-placed in the Albanian Journal of Irreproducible Results (or whatever)." Once you have an internally consistent view on the paper, again, I see no problem with communicating this to editors, and you are doing the author a favor, since the second review is very quick.

In fact, in many cases, editors work on multiple journals, and I have heard of papers being submitted to (eg) Annals, and then being accepted to (eg) the Albanian Journal of IR. Presumably, this makes the author reasonably happy, since the paper actually appears somewhere in finite time.

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I like how people use Albanian = Obscure. – Gjergji Zaimi Feb 22 '11 at 0:48
Gjergji: You mean "like", right? – Sándor Kovács Feb 22 '11 at 1:07
Well... yes. :-) – Gjergji Zaimi Feb 22 '11 at 2:56

I have had similar experiences to the OP and I think the OP is handling it correctly. If I'm rejecting a paper which is (apparently) correct and new on the basis of an opinion that the result is not good enough for journal X and I get it again from journal Y of a similar quality as X, then clearly I have a different opinion from the author about the paper's quality and I think the author deserves a second opinion.

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Um, no. I disagree. I think this is a misunderstanding of the peer review process. The referee is neither accepting nor rejecting the paper - the editor does. The job of a referee is to write a convincing argument which the editor may believe. Writing "I think this paper is weak" won't do. Also, different editors in different journals have different standards. However, if you wrote a solid argument explaining why you think the paper is weak, just mention this is a resubmission and your job is done. If the editor feels the paper deserves a second opinion, she/he will solicit it regardless. – Igor Pak Feb 22 '11 at 18:34

Note throughout that there are two only-partly related issues: literal correctness, and "importance", and that the latter is tangled up with "status" and "relative prestige" of journals. And, don't forget, all journals get far more excellent papers than they can fit into their "pages", so they will reject many excellent ones, for essentially random reasons... because, looked at bluntly, the job of an editor is to reject papers (not to accept).

It is also the job of editors to maintain or enhance the reputation of their journal, while the real reason mathematicians "need" to publish is to maintain or enhance their reputation, and there's a delicate dance done to see who benefits and who "sacrifices", reputation-wise. In that context, I'd tend to bet that confessing prior rejection wouldn't help anything at all, since it resembles telling someone that you didn't really want to go with them to the prom, but you'd already asked other people and were refused.

In that context, I think one should decline to referee a paper a second time for a different journal, if only on the principle that it might be that one gives a negative opinion for (accidentally) subjective reasons, e.g., that the author's priorities are not what they ought to be. One may truly believe this, but declaring that the author should have written a different paper entirely is a hard objection to meet. If the objections are arguably "objective", that there're serious tangible errors, mistatements of fact, disregard of prior art, etc., that's of course a different matter, but I think these pseudo-objective concerns are not the usual watershed for publication-or-not. It's status/reputation.

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I actually have gotten a referee report that roughly said "When I read the title of this paper, I thought it would be about X. Why didn't you write a paper about that instead?" – Ben Webster Aug 6 '11 at 15:37

I agree with Felipe. When a mathematician resubmits a paper to a different journal, she is soliciting a second opinion, as I think is her right. If there was a clear, serious error that you found the first time you refereed a paper and you still see it in the second version, then I think it would be helpful to communicate that to the editor. But I would guess that's a relatively rare situation: most papers are rejected because the referee just doesn't feel they are up to the journal's snuff. Get someone else to decide this the second time.

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I agree with the side saying that you should do the refereeing for the second, third, etc time if you are asked. In particular I very much agree with no name and Ben in the reasons they cite.

I would add the following. Very often there are only a few people who can truly evaluate a paper's worth. If you are one of those and you decline refereeing the chances of the paper going to someone who has much less perspective on the field is higher. Then some decision will be made, possibly taking much more time and it is not necessarily a better decision than what you would have suggested. If independent editors pick you as the best choice to do the evaluation then you probably are (at least one of) the best to do it.

I suppose that when you decide to suggest rejection of a paper you do that based on the quality of the paper versus the quality of the journal. When you are asked to do the same for a different journal this comparison changes and so it is possible that you would feel that the paper is appropriate for the second journal and suggest that they accept it. You could actually try to influence this in your initial opinion. When you suggest that they reject the paper you could give an example of a journal that you feel is appropriate.

Regarding the statement that submitting to a second journal is like asking a second opinion I am not sure that I agree. On one hand we would all like to ask for a second opinion when a paper of ours is rejected, but fortunately we cannot do that. However, we would still like it to be published, so I think it is more like a second shot then a second opinion.

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It seems worth adding that if one was in the situation of being asked again to referee a paper, but the author has acted in good faith and made changes to the paper which have improved its mathematical content and/or exposition, you owe it to him or her to at least rewrite your review taking these changes into account no? I think in this sense you should be giving at least a revised opinion which while not a second opinion is at least something! – Kevin McGerty 0 secs ago – Kevin McGerty Feb 22 '11 at 0:29
Kevin, I totally agree, but I don't see why you are assuming that I don't. – Sándor Kovács Feb 22 '11 at 0:56
p.s.: If the author has substantially rewritten the paper then it is almost a new paper and they should indicate it when submitting. Possibly giving it a (slightly) different title to prevent rejection based on the old version. This seems borderline irrelevant to the original question. On the other hand, if they simply followed the suggestions of the referee and nothing more, then presumably the referee's opinion for the original journal would be the same since otherwise one would expect that their first opinion would have been a conditional acceptance. My point is new journal, new rules. – Sándor Kovács Feb 22 '11 at 1:04

To add a little balance to what Felipe and Pete say (and comparable to what Ben says), if you feel your paper has been acceptably refereed modulo the issue of whether nor not it is appropriate for the journal that it was rejected by: meaning you're confident the referee understood the paper and the context, then when you submit to a 2nd journal it makes sense to mention that it was previously rejected, and give the name of the journal it was rejected by. This makes the editor's life much easier and I think it's appreciated. If you feel you're being persecuted I suppose this isn't a route you're inclined to take. But then again, if this route succeeds you'll quickly discover you are not being persecuted.

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Or you could always resubmit to Rejecta Mathematica :) – José Figueroa-O'Farrill Feb 22 '11 at 0:05
Ryan, I don't understand how mentioning where it was rejected from would make things different other than planting the bug in the editor's ear that there is something wrong with this paper. Since the new editor is likely different than the previous one, this one has no way of knowing who had been asked to referee this paper earlier. So it could go to the same referee and you could be still "persecuted" aided by your own damning of the paper at the start. I bet many editors, if they knew who refereed the paper before, would ask the same referee if they think it is appropriate for their journal. – Sándor Kovács Feb 22 '11 at 3:19
I also think this just has downsides. It could also be the case that after getting rejected by journal A, you submit to journal B, which you and the referee consider to be an inferior journal. However, the editors believe their journal B is on par with journal A (or wants to increase it's standard and from now on be on par with A - and which journal doesn't want to raise its profile), and thus the paper gets rejected automatically. I am not inventing this problem, I know of a case where this happened. (In this case, the editors incidentally knew that the paper had been submitted to journal A.) – Arend Bayer Feb 22 '11 at 13:00
@Sandor, papers are not rejected solely for being wrong, they are rejected sometimes for not fitting the current situation of the journal. AByer's comment "I know a case where this happened" is kind of conspiratorial. I can also give you cases where the editors were happy to know the paper was rejected at another journal and why -- it allows them to perhaps take that into account and either use the previous referee's comments as a basis for acceptance or to seek out a new referee. If you submit to a journal and give no history, it's very likely the editor will find the previous referee. – Ryan Budney Feb 26 '11 at 17:45

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