[jsonau]

Cheapest method: Assume the government really want this number, they can have all mailman help keep track if there are leftover mail(a letter is created/given if resident has no mail) after x days.

Technology wise, I cannot think of an easy and cheap way. Camera with vision for each residential door will be a robust approach. Accuracy can be precise by more investment in software from detecting opening-of-door-event to facial recognition of the expected household members.