Found on the Internet.
Reasons not to allow polygamy:
1. Socially disruptive. Polygamy tends to allow high-status males to monopolize females. This limits the chances for lower ranking males to marry and reproduce. I’m not keen on having a society where Donald Sterling has twenty wives while a mathematics prof has none.*
2. Dysgenic effect: Polygamous societies favor men with capital; hence, older men (who have had more time to accrue wealth and power) tend to have the most wives/children. Older men have higher mutational loads in their sperm. Hence, polygamy diminishes human capital in the long term.
* Another thing to bear to bear in mind is the fact that polygamous societies tend to be both highly dysfunctional and highly authoritarian. Cf , for example the polygamous Mormon enclaves, polygamous societies in Black Africa, etc. I’m not keen on emulating them.
Not only that, but polygamous societies are also reactionary. Ever heard of a progressive polygamous society? No such thing.