I like how the power roles between the sexes on the moon are reversed too. The matriarch has all the power because women are scarce and they take on many husbands out of this need. They always hold the cards and culturally everyone accepts this.
Also, because the value of women is so high no man ever dares attack one less they be sent out an airlock. It is cultural justice. No trial. A man just knows that if he is seen assaulting a woman, he is dead. The community can't afford to lose a single female.
Plus with all the talk of the A.I. Armageddon the book plays right into that discussion.