Polygamy is on trial in Canada, where one of the issues is what justifies anti-polygamy laws infringing on the choices of consenting adults. Advocates of the status quo say polygamy hurts society by creating more unmarried men, who are unhappy and violent, and by making men compete more fiercely for women’s admiration:

Does polygamy between consenting adults harm anyone else? The question has been raised in Canada, where polygamy has been illegal since the nineteenth century, but the supreme court in British Columbia is going to have to decide whether this law is unconstitutional. Doesn’t it infringe the right of adults to arrange their lives by mutual consent? The original law was directed against Mormons, and the present test is also directed against a polygamous fundamentalist Mormon commune. …

There has been one brief filed against decriminalising polygamy … from … anthropologist Joe Henrich. … [He says] monogamy gives huge advantages to societies which practice it. It arose, like philosophy, among the Greeks, passed through the Romans, and then the Christian church took it over as an ideal and managed over the course of around a thousand years to establish it as the norm in Europe, even for the aristocracy. ….

Men who fail to get wives will be driven by competition that it increasingly dangerous to society and to themselves. … Unmarried men are more violent and more generally criminal. … The worst affected are the poor and uneducated. … Because the competition for women is so fierce, making them valuable objects rather than loveable people, men … must control them more carefully. The same dynamic places pressure on the recruitment of younger and younger brides into the marriage market. … Finally, the men will reduce their investment in any particular wives and children. … because they will increasingly spend their efforts on getting more wives rather than looking after the ones they have.

Henrich argues that these factors help to explain the measurable economic failures of highly polygynous countries, including low saving rates, high fertility, and low GDP per capita. … Monogamous marriage has unobvious advantages. In fact he considers that it was the seedbed of European ideas of democracy and, later, human rights and women’s equality. (more)

I very much doubt the Greeks invented monogamy, and the rest of this seems also exaggerated. But such arguments seem worth considering, as a US legal suit to allow polygamy would probably face similar complaints.

Note that such arguments, that polygamy creates more unmarried men, who are unhappy and violent, and makes men compete more fiercely for women’s admiration, also support other laws.  For example, they support laws prohibiting lesbian female relations, or more generally prohibiting women from remaining unmarried to any man.  After all, unmarried women just as directly cause unmarried men, relative to polygamously married women.  Yet there is little political support for such prohibitions.

[Added 7a:  These anti-polygamy arguments also make good pro-polyandry arguments, since men who share a wife are also no longer unmarried men. Added Thurs: They also argue for prostitution.]

These anti-polygamy arguments also support more vigorous punishment of extra-marital affairs. After all, men whose wives cheat on them also get unhappy and violent, and the prospect of inducing wives to cheat makes men compete more fiercely for their admiration. Yet not only does our formal law have only weak punishments for such cheating, it actually goes out of its way to prohibit what would be the naturally strong punishment of blackmail. And our informal social norms regarding cheating spouses usually advise others to “stay out of it.”

It seems to me pretty obvious that we prohibit polygamy mainly because the folks who want to do it (rural religious communes) have low status in our society.  Also, since high status folks cheat and don’t want that discouraged via blackmail, we prohibit blackmail.  Yes there is an element of inertia, but gays have overcome such inertia in ways that polygamists can’t. Gays are common in high status communities and professions; for our elites, many of their best friends really are gay. Not at all true for polygamists.

More interesting data from WrongBot reviewing the book Sex At Dawn:

The book’s first section focuses on the current generally accepted explanation for human sexual evolution, which the authors call “the standard narrative.” … Men are attracted to fertile-appearing women and try to prevent them from having sex with other men so as to confirm the paternity of their offspring; women are attracted to men who seem like they will be good providers for their children and try to prevent them from forming intimate bonds with other women so as to maintain access to their resources. …

[Against that, the authors] offer a wealth of examples in support of their thesis — that in the human evolutionary environment, communal sexual behavior was the dominant paradigm. …

We … take it for granted that any given individual can have only a single father, [but] this was not established scientifically until the 19th century. … [But] dozens of South American tribes (both foragers and farmers) … believe in partible paternity. …. Chimp and gorilla mothers never allow other females in their tribe to hold their young children … Yet, in 87% of human forager societies, mothers are willing to allow other women to breastfeed their children. … Well-respected anthropologists … are in the habit of declaring that marriage is found every human society. … [But] anthropologists are willing to consider all kinds of arrangements to be “marriage”, though, creating confusion that is easily amplified by imprecisions of translation.