We have to calculate quality parameters for each department and to each district. And again the average quality of district is not the average of quality of its departments. As they are not equall....
That's why American President election system (electoral college) works how it works - giving advantage to small states.
The goal of having such a system wasn't getting a population-proportional representation in the first place to my understanding. I think the goal was to don't let the highly populated states dominate leaving the small ones out.