Jumping mro from Counter to past dict directly to object seem like a bit of hack, one that we might regret for subclasses using super() Also, the current docstring is useful. If you really have to change something, we could just delete lines 733 and 734, leaving the instance() check for _eq_(). But that does mess-up the parallelism a bit and it looks odd so I would rather not do that either.

If you want to keep the docstring and make __ne__ subclass friendly, you can reimplement the logic of object.__ne__:

    def __ne__(self, other):
        'True if any counts disagree. Missing counts are treated as zero.'
        eq = self.__eq__(other)
        return NotImplemented if eq is NotImplemented else not eq

or better reuse object.__ne__:

    def __ne__(self, other):
        'True if any counts disagree. Missing counts are treated as zero.'
        return object.__ne__(self, other)

But would not be better to improve the object.__ne__ docstring so that it will be good for Counter and all other classes with customized equality comparison? BTW the current docstring of object.__ne__ is not correct because the special method can return NotImplemented.