This can go beyond the actual assigning/completion of tasks. There’s a mental load that is carried by the person that ‘notices’ the things that need to be done and then is responsible for getting the materials from the store, planning to do it or assigning it to another person. There’s these ‘fairplay’ cards that ive been seeing a lot lately. They help people cohabitating realize and communicate about ‘all’ of the things needing to be done around the house, and each person takes on ‘set tasks’ from start to finish.