def union_update(self, *others):
        r
        _elements = self._elements
        _total = self._total
        for other in map(self._as_mapping, others):
            for element, multiplicity in other.items():
                old_multiplicity = _elements.get(element, 0)
                if multiplicity > old_multiplicity:
                    _elements[element] = multiplicity
                    _total += multiplicity - old_multiplicity
        self._total = _total