What is the term for a society or family in which authority is held by females?

Kay is a thoughtful and considerate person but has a difficult time making decisions on her own. she relies on her one best friend, someone she has known since childhood, to give her advice on virtually every decision she makes. sometimes kay even asks the friend to make the decision for her. at work, she holds a position far below her potential and has refused several promotion opportunities. she is most likely suffering from personality disorder.