Is there any evidence that double blind peer review systems are beneficial? Every so often, I stumble upon a question concerning "double blind peer review", i.e., the authors don't know the reviewers (as usual) but also the reviewers don't know the identity of the authors.

It's always struck me as a rather odd system, with no discernible benefits (because I am under the impression that it's often rather easy to determine who the authors of a paper are anyway), and the creation of dozens of problems with people always being worried of somehow "breaking" the double blindness. (It is not helped by the fact that this would be impossible to implement in my field, math, where everyone posts their preprints on arXiv and people don't hesitate to give talks about unpublished papers).

Is there any actual, scientific, serious research into evaluating the benefits of this system? Or is it all just inertia/tradition/good intentions? I'm not talking about armchair justifications for it with no data to support it.
Yes, there is scientific research on this topic. 

Using data from ACM WSDM'17, A. Tomkins et al. showed that double blind reviewers are less likely than single blind reviewers to accept papers from famous authors, top universities, and top companies.

See: http://www.pnas.org/content/pnas/114/48/12708.full.pdf

Update: As mentioned by @thomas-supports-monica in the comments, there is some evidence that the article linked above may have some issues. See https://papers.nips.cc/paper/8770-on-testing-for-biases-in-peer-review.pdf .