Polygamy is not a good idea as it causes a shortage of available wives.
Boys and girls are born in roughly equal quantities, so if follows that if you start giving more than wife to particular men and one man somewhere is going without.
When a whole society is doing this, and not just the head honcho at the top, you have a huge pool of angry and restless and potentially violent young men. Basically, women will become luxury items because this artificial scarcity means like anything else that is rare, they will be exchangeable for a high price (dowries) so the temptation to commoditise them will be immense (especially true in poorer countries.)
As for the women themselves, they will be locked up in the house as the risk of them being kidnapped is so great (Middle East esp, India and China increasingly, although this is due to female infanticide not polygamy in the latter two cases...) and severe restrictions will be placed on their social behaviour.
Like any 'luxury goods', they will be hoarded by said head honchos as visible proof of the honcho's wealth and status, as mentioned above. This means that only an increasingly tiny minority of wealthy men will be able to marry at all and so pass on their genes.
In most human societies wealth concentrates itself in the hands of just a few families. In female-limited societies, this means only certain families will manage to reproduce as only they can afford to purchase breeding stock for their sons.
Leaving aside what other abnormal stress responses all this will cause in society (resentment and violence against women being the main one) what this does to the male side of the gene pool doesn't bear thinking about...don't forget, humanity has a tiny gene pool compared to most other mammals and we cannot afford to do anything to reduce it still further.
The way the polygamous Middle East / North African Arab/ Arabised societies used to get round this was by kidnapping African, Hindu and European women for the slave trade. East European women were particularly targeted during the Ottoman Empire, for instance.
Polgyamy is a great social evil and I am amazed people still don't understand this.