One of the biggest problems in relationships is a lack of communication. Whether it be about expectations, wants, needs, or even hopes, we have gotten very good at not communicating with our partners.
Considering the divorce rate in todays world, it is not surprising that other types of relationships fail as well. But i think there has been little valid research into the long term potential of poly relationships.
I'm taking a different tack in this reply.
The problem with poly relationships is that they society-destablizing. Let's transfer the liberty-socialism argument from economic into the marriage realm. Modern marriage is very socialistic - very egalitarian. One woman for every man. Poly relationships are very liberty enhancing, winner take all. Seven women for one man who wins at this game and no women for seven men, creating seven bitter losers in this game. This is very destablizing to society - single men with no female anchoring them cause a whole lot of trouble. Look at what the Mormon cults do with their Lost Boys - they boot them out of their micro-society. How does that work, how is it scalable, to the broader culture? To which location would America boot all it's young boys?
First of all, I am not suggesting that poly relationships are for everyone. But then, neither is marriage.
The difference in the Mormon cults is that it was mostly arranged marriages. That is a polar opposite from what I am talking about.
Also, the poly relationship is more dynamic. It allows change without destroying the primary relationship. It allows both partners to enjoy the relationship without sacrificing what they need in their life. It also removes the entire problem of infidelity. Imagine if one not only didn't hide a new romantic relationship, but shared it with their partner. The suspicion, jealousy, and damage done would disappear.
As I have said, this is not for everyone. It takes someone without jealousy or at least willing to control it, to work.
I do not believe it would work for the majority of our society. But that does not mean it should be illegal for those who choose to do so.