Role of a Product Owner
A Product Owner’s job is to own the Product Backlog. Anyone can suggest tasks, but it is the Product Owner who assesses which tasks ought to have priority, and responds accordingly to changes in the business that mean a switch in priority. In business, this really helps with making sure there’s someone who has the final say about what should get done first.
For doing Home Scrum, there isn’t usually a space for having one person act as the Product Owner, because it probably isn’t just one person’s job in the household to dictate what is important for everyone to do. Francis and I have certainly never found a good way of applying the concept, although perhaps it could work for specific areas for a parent to take ownership for an area that affects the children. Even then, I would be careful not to stifle anyone’s sense of autonomy and ownership over what tasks they have agreed to do.
You could also experiment with sharing the role of being a Product Owner; perhaps one person is Product Owner for one Sprint and someone else is the next. Or you could see if it works for your team to share out ownership over a particular life category to different people, so perhaps one person is in charge of prioritising the tasks coming up for the ‘Dog’ category, while someone else is the Product Owner for the ‘House’ category. It all depends on what works for you.