If women ruled the world

I'm going through my Hawaii pictures right now, and I just came across a picture from when J. and I went to Jamaica in June. We swam with sting rays.

The ray I'm holding is female. The males are smaller - a largish male is about half the size of the ray I'm holding. Which makes me wonder:

In nature, it seems that females are usually stronger, larger and dominant. But, when it comes to humans and what we value in western society, the ideal woman is smaller and more submissive than her male counterpart. Do we have it backwards? Should women be the ones to rule the roost?

I know it exists. Some native american tribes were matriarchal. And, have you seen a traditional asian family? Grandma bosses everyone around.

So, do we have it wrong? After all, I'm sure you've heard "If women ruled the world, we would have no wars." But, is it true? Certain events run through my mind -- the Crusades, Jihad, and American Oil Wars... What would the world be like if women ran it?