Now that is entirely possible, but I still don't think that house ownership is going to change anything -- especially not shared ownership.

I will admit to a strongly-held position, based on my own upbringing: I will not clean up after a man, nor do I think women should -- not when it means that the woman has the major burden of homemaking/housekeeping. It's one thing if homemaking is her job, so that she spends most of her time creating and sustaining the home, while he spends most of his time making the money that enables them to have a life, or if she does the inside work while he does the outside work, and the amount of work is roughly equivalent. What commonly happens, however, is that while both partners have equally demanding paid jobs, the woman takes on the vast majority of the home work, and ends up contributing far more time and energy than the man does. Even if he takes on the "outside work", it rarely takes as much time as the "inside work".

I don't have the studies at hand, but I believe this phenomenon is well-documented.