After reading a couple of these answers, I started thinking about the larger, evolutionary significance of of jealousy. Right now, jealousy supports pair bonding and the nuclear family as the unit for raising children. Without jealousy, people would no longer feel an individual sense of ownership of their partners or of their children.
Rather, if the society were to survive, the idea that it takes a village to raise a child would become literally true. Everyone would have to be responsible for all the children, regardless of whether they had a genetic stake in that child. The bonds that tie together pairs would be shifted to a larger group.
In such a society, there would probably be a lot more sharing of partners. No one would feel like they owned anyone else and no one would be jealous of anyone else having sexual relations with anyone else. I think the Bonobos are supposed to be like this.
It seems to me that people would form large extended family groups. The groups would be of different sizes. I think small groups would be around ten to fifteen people and larger groups of maybe around thirty people. I think there could be even larger groups, but that would probably fairly unusual.