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I believe that I'm in a rather unusual situation and, as the title suggests, there is some uncertainty about how I should acknowledge a particular referee. This referee was supposed to be anonymous, but clearly (and deliberately) identified themselves in their report for historical context.

Should I identify this person in the acknowledgements section, or is it rude to thank the referees collectively without identifying this person?

Thanks.

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    If in doubt, ask them directly. – Boris Bukh Oct 23 '17 at 23:58
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I agree with @Boris Bukh's comment: as a general rule, feel free to acknowledge whom you want...but if there is any real worry that your acknowledgment could be received unfavorably, ask the acknowledgee first.

I think yours is a "nondegenerate case" of that above principle. In particular, by choosing your language carefully, you can acknowledge the non-anonymous referee without disclosing that they were a referee. E.g. you could write "I would like to thank A. Professor for XX. I would also like to thank the referees for YY." As long as XX does not equal YY, you are not being dishonest or misleading; you are just choosing not to reveal certain information. (If XX equals YY, it's not so clear why you need to acknowledge A. Professor by name.) If you decide to do this, sending the proposed acknowledging text to A. Professor for their approval might be a good idea.

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If a reviewer chooses to be non-anonymous, I think you can directly acknowledge them.

There is a precedent for this. In the Copernicus journals by the European Geophysical Unions, the LaTeX template contains a command for "thanking the reviewers". Reviewers can choose to be anonymous or not. All invited reviews are public, so anyone can read the review and confirm the anonymity or name of the reviewer. If I recall correctly, there's actually different commands (or different arguments, I don't remember) depending on whether or not they chose to reveal themselves. My colleague published a paper where one reviewer revealed himself (he is a well-known senior scientist) and the other did not. The acknowledgements, which were added by the publisher in the typesetting phase, were formulated something along the lines of The authors thank James Doe and one anonymous reviewer for their peer review.

I don't see why it would be a problem to write this yourself.

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I'd thank "the reviewers".

I had the case recently where I guessed one out of three anonymous reviewers (small community, someone I had already a discussion about my work, and from a group likely to be asked for a review given the topic). Even before I returned the revisions, we had a conversation in which they identified a second reviewer (also guessable - distinctive style :-) ). I just thanked the "anonymous reviewers". If the conversation with the first reviewer hadn't happened, I'd have thanked them by name, but their status as a reviewer exempted the previous helpful (mostly just encouraging - it was my first paper) conversation. Also, you could ask.

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Can you explain "for historical context?"

Do you mean this referee was suggesting edits and justified the request by pointing to his/her own publications? If this is the case, you might want to adopt the references that were suggested, thus citing him/her, but not acknowledge the person separately as a referee. If he or she provided above/beyond background, methods, or advice then it should be attributed appropriately in those sections.

But more broadly, if the policy is for blind review the referee's choice to break the blinding privately does not necessarily give you the right to also break the blinding publicly. I would thank them collectively for their work, as was the original intent.

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