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I have received requests to referee three different papers by a certain author in the past year (one of them twice, after it was rejected from the first journal). I work in applied mathematics, and in my field three to four papers per year is the typical output of a reasonably prolific author (excluding those who manage a large research group).

I am starting to think it would be fair to decline the last review, because I don’t want to have too large an impact over the career of this author. Moreover, I believe that having a variety of opinions would improve the general outcome of the reviewing process. Is my reasoning sound? Is “I’ve already reviewed many papers from the same author recently” a valid reason to refuse? Is there any good way to decide how many is too many?

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    It is your time - you can spend it as you wish. You do not need a "valid reason" to refuse a request. That you don't want to do it is more than sufficient.
    – emory
    Jan 26 '18 at 22:18
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You don't say whether you've recommended the papers for acceptance or rejection.

If you've recommended them for rejection (but nevertheless you view the work as being a reasonable specimen of the form, i.e., not egregiously flawed or crankish), then I think your idea to spread the opinions around is a good one. Sometimes I get sent a paper for which I think "I don't value this paper much, but so far as I know someone else really could." In that situation I often decline to referee it.

If you've recommended both of them for acceptance: well, you would think the same argument should apply, but I don't find it as compelling! Rather than declining to referee, you could just continue to read carefully and not assume the work is good because you found the prior work to be good. And if you really have a clear idea that the author is consistently doing good work -- there's no conflict of interest there! By consistently recommending their work for publication, you are helping them out but also the field.

Is “I’ve already reviewed many papers from the same author recently” a valid reason to refuse?

I think so, yes. In fact almost anything is a valid reason to refuse in the current climate: so many papers are being written and processed at this point in time that anyone person has to limit their involvement. Editors are getting turned down by referees all the time. If you decline, do it quickly and suggest other possible referees, in all my experience they won't bat an eye. As to

Is there any good way to decide how many is too many?

I think it has to come down to your own judgment, because (of course, right?) this also depends on your other professional responsibilities. As has been discussed on this site before, try to apply golden-rule considerations to your general refereeing policy.

Having said all that, I did want to make one counterargument: in all parts of mathematics in which I am familiar (which ranges from very theoretical to very moderately applied), refereeing papers takes a long time in part because the task truly is very intellectually demanding. For a given paper, there are a number of people whose expertise is so unusually close to the topic of the paper that they can evaluate it much more easily and quickly than most other experts in the same area. In many parts of mathematics, this number is very small -- sometimes, unfortunately, it is zero. If you are part of a cohort that has unusual facility and ease with the author's work, then maybe you can do in a day or week what some other (expert) mathematician would take months to do. In that case you should think again before declining, it seems to me.

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    To add to the rejection case: if you've recommended them for rejection, then you probably find those papers not worth reading, so it probably won't be worth your time to read another paper by the same author.
    – Kimball
    Jan 26 '18 at 15:37
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    I happen to be in the "counterargument" class. I currently enjoy researching in a topic that is very specialized. Only a few people other than me have published on it, and the last year or so has been particularly productive for me. I've suddenly found myself seeing my papers have a significant issue with finding reviewers. I can't say for certain why that is so, of course, but possibly that small number of people familiar and presumably interested in the topic have been declining. I'm looking at really long publishing times, even by pure mathematics standards, one way or another.
    – zibadawa timmy
    Jan 26 '18 at 21:40
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    I recommend rewording one sentence above to "By consistently recommending their work for publication, you are helping them out but also the field." There is no gender information in the OP, and we shouldn't assume that an applied mathematician must be maie.
    – Greg Martin
    Jan 27 '18 at 9:58
  • @GregMartin The consensus on Meta seems to be "let the author decide which pronouns they prefer, and don't insist for them to be changed".
    – Federico Poloni
    Jan 27 '18 at 10:43
  • Hence "recommend" and not "insist". The fact remains that gender bias is prevalent and ongoing in STEM fields, and defaulting to male pronouns is both a symptom of our own internal biases and a vector by which harmful bias is perpetuated. Most of us observe and bemoan the underrepresentation of women in mathematics (and on websites such as this), yet even the smallest suggestions for actually improving the situation are often treated with hostility ... and perceived consensus on Meta was formed by a community already affected by bias.
    – Greg Martin
    Jan 27 '18 at 18:48

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