Being in a committed monogamous relationship is better than being polygamous. I will begin by laying out a steel-man argument about polygamy.
From an evolutionary biology perspective, a fundamental aspect of living things is ensuring the survival of a species, and sexual reproduction is the means through that is achieved.
Therefore, a strong case can be made that men are naturally inclined to have multiple sexual partners.
A simple logical extension of this would suggest that women possess a reproductive desire to the same degree as men. But women are child bearers, and thus have an asymmetrical need for protection and security. It is not unreasonable to then assert that women have a vested interest in being loyal to one sexual partner, or maybe more than one sexual partner, but probably fewer than the number of sexual partners a man would have.
A stronger steel-man argument can be made for polygamy, but that should suffice.
My argument against polygamy is simple - it's a distraction.
Achieving anything meaningful in life requires discipline, impulse control, and sacrifice.
Being inculcated in polygamy puts you in an environment that fosters instant gratification to such a degree that it permeates every other aspect of your well-being in a negative, and sometimes irreversible way.
There are three scenarios in which your partner will voluntarily engage in a polygamous relationship.
1. Insecurity, manifesting as blind love and delusion. This is amplified when kids are involved.
2. You provide enough material resources such that it overrides your partners' lack of emotional security.
3. Your partner also has multiple sexual partners.
In scenario one, I argue that you can't truly respect someone that has such elastic standards and morals.
In scenario two, I argue that when a better deal comes around for your partner, they are likely to jump ship. Examples of better deals would be :
A) Another polygamous person with more resources.
B) A monogamous person with the same amount of resources.
C) Worse of all, a monogamous person with more resources.
In scenario three, I argue that from a health and safety standpoint, this is unsustainable.