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> It would be interesting to have Counter.elements_count() 
> if it has a complexity of O(1): if the collections 
> maintains a total (in a private attribute).
I agree that it would be interesting; however, it would be an implementation disaster. We would have to override (and slow-down) every mutating method in order to maintain the invariant. And as a dict subclass, any C module using PyDict_Setitem() would bypass those methods and still break the invariant no matter what we do.
The Counter tool was designed in an open fashion (a simple, fully exposed dictionary with a few handy methods for counting). In that regard, it is much different and more flexible than a traditional Bag class that maintains its data privately.