In msg266115, Robert Collins suggested  "add a different name and deprecate assertCountEqual".

In msg266184, Gregory Smith said "not against adding a new name if it makes glorious sense, but we should not remove the old names from unittest as that causes unnecessary pain (based on past experience)."

Others suggested status quo.

In msg352556, Michael Ford said "I like assertPermutation", but did not reopen the issue.

Coming at this fresh, via the PR that patches idlelib, my first thought was that assertCountEqual meant assertEqual(len(a), len(b)).  So the issue seems real.  assertPermutation is much better to me and I would like it added.

In unittest/case.py, PR 16228 renames assertCountEqual to assertPermutation and adds assertCountEqual as an alias, with no plan for deprecation and removal, as eventually done with other duplicates.

However, the PR also immediately renames all instances of assertCountEqual in the stdlib.  Perhaps 1/4 of these are in idlelib tests.  Much as I prefer the new name, this is unacceptible as it immediately makes backporting test changes in these areas (and I plan to make some) a manual process.  So I don't want IDLE tests renamed until 3.8 is off maintenance and the name change can be made in all maintenance versions at once.

I leave it to the rest of you to decide on the rest of the stdlib.