I want to say some things about doubly-anonymous refereeing FOR NO REASON AT ALL AND PROMPTED BY NOTHING.
All research & evidence points to the fact that doubly-anonymous refereeing / judging /etc leads to better outcomes for people from marginalized groups.

"But I want to put my stuff on arXiv right away to claim priority!" I hear you cry.
OK, so @xl772 points out that one option is that journals using doubly-anonymous refereeing have much faster turnaround times.

"Not good enough! I want to put it on arXiv right now! Right when it's done! Because I won the race to solve this SUPER IMPORTANT PROBLEM."
How about this: When you are asked to referee a paper, it comes with a short description of the benefits of doubly-anonymous refereeing w.r.t. equity and a plea to respect the process & not seek to find out who the authors are before you complete the report.
"If it's on arXiv, the ref will know who wrote it b/c everyone 100% keeps up w/ everything posted to arXiv in their field every single day."

Look, I don't fucking believe you. But if you already saw/read/know the work, tell the editor who may decide to send it to someone else.
"Even so, there are telltale signs. The writing style! The subject matter! The approach! The previous work cited!"

OK, but that's at best a guess. And you'd be surprised how often people are wrong when they guess about stuff like this.
"But referees won't respect the process! If it's on arXiv, they won't be able to stop themselves from going to see who wrote it."

If that's true, I don't want to hear another fucking word from any of you ever about how disappointed you are in students who cheat on your tests.
The upshot is: the best case scenario is that papers are reviewed more equitably and our profession is more fair & open to mathematicians from under represented groups & from less posh institutions & who aren't fancy enough to benefit from name recognition.
The worst case scenario is that it's exactly the same as the current system, where the referee knows who the author is.

THE WORST CASE IS NO CHANGE AND THE BEST CASE IS MORE EQUITY.
If you are opposed to this, I really have to wonder why. I kind of think that deep down you know you benefit in some subtle way from the current system.

If I'm being generous, I'll call it inertia. But I don't think inertia is a good reason to resist inclusionary practices.
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