> total should be a cached property, that's updated on every Counter update

That would run into difficulties for Counters with float values: e.g., after

>>> c = Counter()
>>> c['spam'] = 1e100
>>> c['eggs'] = 1
>>> c['spam'] = 0

the  cached total would likely be 0.0, because that's what the sum of the (new-old) values gives:

>>> (1e100 - 0) + (1 - 0) + (0 - 1e100)
0.0