polygamy = how to pee in your own gene pool!
The only rationale/justification I can imagine for polygamy is biological primitive -- it allows a single male to keep a number of breeding females pregnant, so it increases the number of offspring, which is useful for growing the tribe.
However, it is clear that not all males can take advantage of this opportunity, the birth ratio being roughly 50/50. So the long term effect is that it causes young males to be killed or exiled from the tribe to reduce competition.
From a social (not biological) point of view, it's just stupid and destabilizing.
OTOH, balanced with an equal amount of polyandry (multiple husbands for a single woman), it could work out in an interesting way. Look at polyandry pragmatically -- the men can cooperatively trade off responsibilities: my week to work, your week to take out the garbage and mow the lawn, his week to paint the porch. No one man gets burned out.
[Joking! I'm joking!!!]
Families were meant to be one man, one woman.
What kind of craziness is next???