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A week ago, I have received an invitation to review a manuscript in Applied Mathematics by an Elsevier journal and I was given a deadline of two weeks to reply to the invitation. As I was a little bit occupied, I have decided that I will respond to the invitation a week after receiving the invitation, in order to scope through the abstract.

When I logged into the system a week later, I noticed that the paper was submitted two months earlier and the editor accepted it for publication with only one referee report, which was positive. This acceptance happened approximately a week after inviting me.

Going through the manuscript now, I have some minor comments about the paper, but what I need to know is if it is a common practice to accept a paper with one report, even when dealing with applied mathematics papers rather than papers in pure mathematics.

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It is normal to solicit more than one review of a paper. Its perfectly normal for the editor to decide to publish if only one of the two reviews is positive, and the editor feels the positive reviewer has the more reasonable case (or vice versa). Its not common, at least in my field (not quite applied math) to publish if only one review has been recieved. However at some journals, its considered acceptable to only have one external reviewer if the editor is an expert in the topic of the paper, with the editor effectively acting as the second reviewer themselves.

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    The editor may have also carefully read the paper themself. I often do that if it's in an area I'm interested in knowledgeable about. Jun 11, 2023 at 22:48
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    I have edited the title of the question to match the question in the body of OP. This might affect your answer.
    – Ben
    Jun 11, 2023 at 23:09
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    @WolfgangBangerth I did say that, more or less. Jun 11, 2023 at 23:10
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I don't think it is common practice. Regardless of the field, I think it might be a waste of time to invite multiple reviewers and not waiting for all to respond. It is just two weeks, this is already a rather short period of time! What if you invested a substantial amount of time reviewing the paper or you found issues that require major revision?

I also consider this behavior by the editor as impolite with respect to you as a reviewer.

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I don't know what the typical timelines are in applied mathematics, but based on your description, what you experienced is highly unusual.

Usually when editors invite reviewers and ask for a response after X time, they will wait X time before doing something. So the fact that your editor did something before X time passed is already unusual. If it happens, I would guess that they are making an accelerated decision for whatever reason (e.g. they received confidential information that made further review unnecessary) - but in this case the result is likely to be 'reject'. That you see an 'accept' decision is unusual.

It could be that the journal is one of those hyper-accelerated ones where they prioritize the time taken from submission to decision, but even that would be unusual, because such a journal is very unlikely to give you two weeks to respond to the review invitation. Two weeks to submit the review, maybe, but not two weeks to accept/decline the invitation. In fact, it's unusual to give you two weeks to accept/decline; usually there is no deadline to respond.

Other unusual things in your description are 1) you are apparently able to see the other reviews before submitting your own, and 2) you are apparently able to submit a review even after an accept decision is made (usually once an accept decision is made, all outstanding reviews are cancelled). Even your decision to respond to the invitation a week after receiving it is unusual (usually the probability of a reviewer responding drops rapidly with time, unless a reminder is sent).

So: everything in your description is unusual.

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