Lightening rod's Polygamy: Polygamy and Underpopulation

Polygamy & Underpopulation

Against

Rivalry of spouses
Unsure of father (if multiple husbands)
Do you want to allow polygamy for both sexes or just one
If balanced or small difference in sexual population than argument that both must practise so all can have mates.
Large families harder to care for and instruct properly vs small family
In a small population is there enough diversity or people to avoid a lot of inter-marrying.
It has been said theorized that a lot of inbreeding(marrying close relations) can corrupt the genes causing the genes to grow weaker and cause genetic problems.

For

If one sex has significantly more people than the other sex either naturally or unnaturally like war. Polygamy is one solution where everyone who wants a mate can get one. Without polygamy the excess either can not mate, compete for the existing minority sex to the point of trying to steal others mates. A current example is Tibet. Where some women but not many and only under certain conditions have multiple husbands.
Another time polygamy is useful is with a limited gene pool. Ex from tv Star Trek Next Generation they merged two groups of people. The one side had only 5 different gene sets which were degrading fast in offspring(future generations)and the other was a diverse small group needing a place to live. So, Capt. Picard's idea was to merge them together and allow each person from the second diverse but small population to have 3 spouses as a way to maximize the new gene pool.
In old Jewish days a man would marry his brother's widow if she had no offspring in hopes of continuing the line.
Also a man was allowed to take another wife, if his first wife was barren.
Family lines are traced by offspring and if there is no offspring the line dies.