question for the masses

So, dear, lovely, awesome, unparalleled ladies of my flist I come here today to suck up to you ask you a very serious question of great import: what do you think a matriarchal society should have/be like/work like? Why? (okay, so two questions, then).

I'm sort of playing around with world-building sandboxes and this may never percolate into anything beyond a mental exercise, so be warned. However, isn't this a great mental exercise? (hint: it is)