What would society look like if men were not in charge?

[KurtNYC]

31. The Iroquois, from whom we got the Senate and House representation system was mostly matriarchal

The Iroquois are a Mother Clan system, which is gender equal. No person is entitled to 'own' land, but it is believed that the Creator appointed women as stewards of the land. Traditionally, the Clan Mothers appoint leaders, as they have raised children and are therefore held to a higher regard. By the same token, if a leader does not prove sound, becomes corrupt or does not listen to the people, the Clan Mothers have the power to strip him of his leadership.

When Americans and Canadians of European descent began to study Iroquois customs in the 18th and 19th centuries, they learned that the people had a matrilineal system: women held property and hereditary leadership passed through their lines. They held dwellings, horses and farmed land, and a woman's property before marriage stayed in her possession without being mixed with that of her husband. They had separate roles but real power in the nations. The work of a woman's hands was hers to do with as she saw fit. At marriage, a young couple lived in the longhouse of the wife's family. A woman choosing to divorce a shiftless or otherwise unsatisfactory husband was able to ask him to leave the dwelling and take his possessions with him.

The children of the marriage belong to their mother's clan and gain their social status through hers. Her brothers are important teachers and mentors to the children, especially introducing boys to men's roles and societies. The clans are matrilineal, that is, clan ties are traced through the mother's line. If a couple separated, the woman traditionally kept the children. The chief of a clan can be removed at any time by a council of the women elders of that clan. The chief's sister was responsible for nominating his successor.

http://en.wikipedia.org/wiki/Iroquois#Women_in_society

So we just changed women to men and used their 2 house system of representative government.