socket(7) does contain SO_PRIORITY but trying to use this value will result in this error: AttributeError: 'module' object has no attribute 'SO_PRIORITY'

For the record, a little googling indicates this may be a linux-only option (FreeBSD 6.4, for example, does not support it, nor does OS X 10.8, which are two systems to which I currently have access).  That doesn't mean it shouldn't be added.

Here's a simple patch which adds this flag. It has no tests, because I noticed that there are no tests for per-platform flags in test_socket.py (only for CAN, RDS and general flags).

Yeah, I'm not sure how you'd write a test in such a way that it would test anything meaningful.  Parse the .h file in the test?  Seems like overkill.

I agree. The test is not that meaningful. But hey, we have the test that tests this kind of constant.

http://hg.python.org/cpython/rev/513da56d28de

You should also modify Doc/library/socket.rst to mention the new constant in the documentation (don't forget the ".. versionadded::" flag).

Adding a new constant cannot break anything in Python, so I propose to it in Python 3.4.

@Larry (our release manager): Do you agree?

It's *possible* but I'm willing to risk it.  You have my permission to apply that patch.

New changeset 9bbada125b3f by Benjamin Peterson in branch 'default':
add SO_PRIORITY (closes #19802)
http://hg.python.org/cpython/rev/9bbada125b3f

Sorry, this is now too late for 3.4.  3.4 is now in "security fixes only" mode.  This is not a security fix, therefore 3.4 is now ineligible.

Since this change was committed to 3.5, it's better to let the historical record reflect that.  So I'm changing the version back to 3.5 (and not 3.4).