The point of peer review is anonymity but since most authors upload their papers to arxiv long before the paper is published (at least for math, stats, computer science etc), the reviewers should see who wrote the script by simple googling right? Will this have an impact on the review process? That is, a famous scholar's article will more likely be accepted to top journal given similar quality.

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    Interesting, I myself have never been asked to review a paper that was anonymous. I don’t think the point of peer review is anonymity, it’s to review your proposal. – A rural reader Apr 14 at 21:09
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    I'd object that the point of peer review is anonymity, the point is review of the methodology and (to some extent) novelty – Azor Ahai -him- Apr 14 at 21:12
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    Am I lost in the past, or isn't it still the case that most math refereeing is just single-blind (the referee is anonymous)? – paul garrett Apr 14 at 21:14
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    @EthanBolker: I refereed a paper for Proceedings of the AMS a few months ago; it was single-blind. – Jochen Glueck Apr 14 at 22:25
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    No - only a few MAA journals have gone double-blind - AMS journals are still single-blind. – Alexander Woo Apr 14 at 22:26

It is in fact often easy for a reviewer to find out who an author is, unless the author is quite new to publishing and has not uploaded the paper to arXiv.

Sometimes it is hard not to know even without a search since the author may be building on their previous work so the list of references will be a giveaway even if the the text doesn't refer to "my previous work in [reference]".

That said, refraining from such a search is implicit in the unwritten contract between the reviewer and the editor.

I hope and suspect most reviewers honor that contract.

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    +1. Example policy: "As a referee, you are not disqualified to evaluate a paper if you think you know an author’s identity (unless you have a conflict of interest, such as being the author’s advisor or student). The journal asks you not to do additional research to identify the authors." – darij grinberg Apr 14 at 22:51
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    I doubt that experienced reviewers would even bother to try to search out an author. They have better things to do. – Buffy Apr 15 at 14:53
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    In my opinion it can be very difficult to separate "research to identify the authors" from a referee's due diligence on searching the literature. What kind of search for relevant recent work is not going to turn up an arxiv preprint with the same title? – Pete L. Clark Apr 15 at 16:30

This is extremely field-dependent. I have never heard of double-blind reviews in mathematics: never got to referee a paper that had the author's name redacted, never seen a paper where the author made a point of hiding if cited work is indeed theirs (e.g. "X did [1], Y did [2]" instead of "X did [1], we did [2]"). But at least some psychology/sociology journals I know maintain the policy of double-blind review, and I read papers in these fields that were written in third person, as in the example, apparently to conceal themselves. I have my doubts if this can work at all - even if the bibliography doesn't give the author straight away, the reviewer is often expected to check if the prior work in the field is well represented and discussed, which leads to queries and googling, which again can give the reviewer a pretty clear picture who they are reading.

And to comment on the opening of your question: the main point of anonymity of the reviewer is always that they are protected from retaliation of a rejected author, and since the author I am reading may well be my own superior (how many experts on foo of bar are there?), I am glad that I enjoy that protection. This is fundamental for the confidence in the process, regardless of your field.

But the other way round, it is not as clear cut: we all accept end expect the reviewers to give their expert opinion. But in some subcommunities we have agreed that said expert opinion can or should take into account who the author of the paper is, of course your mileage may wary on whether you like it or not. You describe one hypothetical often given (but not as often observed in nature) as an example of corrupting effects of this situation. As a sometimes disgruntled author, completely sure that I would have been accepted for publication if only I had more recognition, I must admit that stories of top journals publishing long series of sub-par papers of famous mathematicians are exceedingly rare, and if happen, tend to end badly for the editors, authors, and sometimes reviewers. I think that for the most part we do believe this market regulates itself, or at least we don't think that the prevailing single-blind in mathematics is the main problem in urgent need to be corrected. But again, your mileage may vary.

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    I have reviewed for and submitted to a journal that does double blind refereeing. I think the goal is to make sure that authors from less prestigious places get a fair shake, not to prevent established people from coasting on their reputation. Whether double blinding makes a difference in acceptance would be hard to tell. – Ethan Bolker Apr 15 at 15:31
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    The journals affiliated with the MAA (Mathematical Association of America) have been double blind for more than five years now. With regard to the field of mathematics as a whole, they are definitely outliers. (In fact I have refereed papers for MAA journals and done just as the author says: found the corresponding arxiv preprint by googling. I find the situation a bit odd.) – Pete L. Clark Apr 15 at 16:23
  • Thank you both for these comments. Though - and I write it with genuine respect for MAA mission and core values - I wonder if we have any example of a cutting-edge narrow-specialization research journal that went the same way. And - was there any reason given when MAA switched to duble blind. There is also the issue that the fair shake for the affiliatly challenged (and I jest only because I am probably one of such people) is not threatened by the reviewer, it is sometimes the editor that desk rejects the authors not glamorous enough for their journal. – lemon314 Apr 15 at 17:18

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