This is not a matter of statistical analysis of how happy people are in polygamous families as compared to monogamous ones. Polygamy leads to certain results because of the way it is structured. Let us say we are talking about a typical form of polygamy, which is the polygynous family. There is only one husband and he has only so much time, 24 hours per day, during which he normally has some kind of work to do - it takes money to support a family, and more money to support a larger family - and then in his remaining time, he will still have his personal interests, the time he spends on reddit and so forth, and of his remaining time, he has to divide that between all of his various wives and children. If he has ten wives and fifty children, that's 60 people hoping to get some fraction of his available time and resources. These are not unrealistic numbers, that is what a polygynous family is like. So how good a husband is he going to be, dividing his time among the 60 immediate family members that he has? Wives want a husband, children want a father. Of course, the children do have the advantage of having 10 mothers. But they still want a father. And father has very little time for them, and will probably find ways to put them to work.

If we compare a monogamous family in which there might be one husband, one wife, and a few children, let's say 5 (same number as what I have hypothesized as the children per wife in the polygamous family) we would see that the husband has tremendously more time as well as money to spend on each individual member of his immediate family. Ten times as much. So that would seem to be an advantage.

You might argue if you wish that the wives can keep each other happy. And the children can play with each other. Of course, they can also fight with each other. They are all rivals for the affections of the very busy head of the family, the husband. And no matter how much this husband may love his wives and children, he is just not going to have very much time for any one of them. He would be lucky if he can even remember all of their names.

So, does that not make any difference to you? What kind of family would you prefer to have had as a child? Maybe you had a terrible father and the less you saw of him, the better. But I think you might not have liked that horde of out-of-control siblings that you hypothetically might have had. So to me, the difference seems obvious.