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I sent a paper to a good journal with other coauthors. Some days ago, one of my coauthors was sent an invitation to review this paper. Is this logical? I mean, has anybody of you ever received an invitation to review your own paper?
Some months ago, the same occurred with another paper in another good journal. I declined the invitation explaining that I was an author and I suggested other reviewers.
But, as I got a similar invitation now, I ask whether this is a usual practice...
It's absolutely not usual practice and a clear case of the editor in charge being asleep at the wheel. This should not be happening: An editor's job is to find impartial reviewers and asking an author (or even someone close to the author) is definitely failing at this job.
Just the same, it is unethical for you to accept such invitations. Politely point out that you are an author of the paper and that, therefore, it would clearly be a conflict of interest for you to review the paper.
I've had this happen before to a coauthor (they were neither the first nor last author in a list of ~6), who contacted the editor replying that obviously they couldn't review the paper.
We had a little chuckle over it and moved on. Probably the editor was a bit embarrassed by their error, otherwise no harm done. I presume they used a list of previous reviewers the journal had contacted on the topic of our paper and missed that they were actually an author on the submitted work, or maybe they made a cognitive switch and started typing a name they just read was an author instead of the reviewer they intended to type.
I think the other answers are being a bit harsh towards the editor: they clearly made a mistake, but no reasonable author would ever review their own paper and this shouldn't cause any real problem. No, this is not a usual practice, but it happens at low frequency when people are busy. It's good you are producing enough work to have it happen to you or your colleagues twice.
As mentioned in comments, if your subfield practices triple-blind review where the editor is blinded to the identity of the authors then it is even more likely such errors could occur (and be less the fault of the editor) if imprecise software is used to exclude possible reviewers.
Obviously, one should never, ever receive an invitation to review one's own paper, since that would make a mockery of peer review. Indeed, reviewing one's own paper is a good reason for retraction.
On a paper with a vast number of middle authors (e.g., one of those 1000+ author papers), I can certainly imagine this happening by mistake. In a typical mathematics paper, however, the number of authors is never more than a handful, and so it would be difficult to make such a mistake without either a) a spectacular degree of inattention, or b) a terrible review system interface.
With a sufficiently lazy or inept editor or with sufficiently terrible software, however, any degree of mistake is possible.
You should state a conflict of interest to the editor.
I am sure they will realize that it is unrealistic to expect you to be neutral while reviewing the paper.
Seriously: They did not pay enough attention. Such things happen sometimes, but you cannot take advantage from it without facing consequences sooner or later.
