Colloquially, at least—that is, in consideration of the fact that I know nobody who is genuinely "happily married", unless they express their genuine happiness by complaining about their marriage and denigrating their spouse all the time—I find polygamy indicative of mental illness.
I realize that's somewhat for comic effect, but it's worth noting that most polygamist marriages exhibit a dramatically different power dynamic. It's more like:
Man: Wife 1 is in charge of cooking, Wife 2 is in charge of cleaning, Wife 3 is in charge of watching the kids, Wife 4 (the new, young one) is in charge of having sex with me. I'll be back this evening, and I expect everything to be in tip-top shape!
Wives 1-4, in unison: Yes, master. We exist to serve you.
So you can see the appeal, at least for chauvinist men. The frequencyof underaged brides in those situations also speaks to certain base motivations. Why the women go for it is less clear (although from my knowledge of these communities, women are typically heavily oppressed and controlled).