The men did, but in my understanding the women had ultimate veto power. If the war chief's ceremonial beads hit the ground, that's a death/banishment sentence. They'd give you two chances to stop doing whatever they didn't approve of, but ultimately if the women said no 3 times, you're a dead man.

The only reason that I don't consider that a bicameral system is that while the men may have been elected, the women were just all the women that lived to a certain age.