Via Tyler Cowen of Marginal Revolution, here's a link to a counterintuitive but compelling argument against the institution of traditional polygamy (that would be polygyny for sticklers but I'm going stick with the conventional term here.)

Cowen links to a Globe and Mail interview of Professor Shoshana Grossbard, an expert in the economics of marriage from San Diego State University by Vancouver journalist James Keller.

[A]llowing men to have multiple wives inevitably leads to a reduced supply of women, increasing demand.

But rather than making women more valuable in such communities, she said, that scarcity encourages men in polygamous societies to exert control over them to ensure they have access to the limited supply.

“In the cultures and societies worldwide that have embraced it, polygamy is associated with undesirable economic, societal, physical, psychological and emotional factors related especially to women’s well-being,” said Prof. Grossbard, whose research has primarily focused on polygamous cultures in Africa.

Prof. Grossbard was the latest academic to testify in B.C. Supreme Court in a reference case to determine whether Canada’s polygamy law is consistent with the religious guarantees in the Charter of Rights and Freedoms. The court will also hear from current and former residents of polygamous communities.

Prof. Grossbard said there are fewer women available to men in societies that permit polygamy – even for monogamous men, because they are drawing from the same pool of women.

Since that scarcity could increase what she describes as the women’s “bargaining power,” men in such societies have an incentive to ensure they retain control over who the women marry.

To that end, Prof. Grossbard said, polygamy is associated with teenage brides, arranged and forced marriages, payments to brides’ fathers, little emphasis on “romantic” love and poor access to education or the work force – all designed to restrict the ability of women to choose who they marry.

“The men in polygamous societies want these institutions to help them control women,” Prof. Grossbard said.

Source: Globe and Mail

In his post Cowen asks

I am not a fan of polygamy, but I find this argument strange (though not strictly impossible; men can behave preemptively and incur a large fixed cost to prevent a subsequent erosion of their control). Surely Grossbard would not argue that all institutions which improve the bargaining power of women lead to...less bargaining power for women. So why is polygamy so special in this regard?

Source: Marginal Revolution

I think Grossbard actually answers the question but since, as I say, it does seem counterintuitive I'm going to give it a shot.  The answer, I think, comes from a common but false assumption about Patriarchy, one shared by both by feminists such as Grossbard and agnostics like Cowen: "Patriarchy" is synonymous with "male dominance."  More often, especially in cultures that also practice polygamy, capital-P Patriarchy is better understood as family domination. (Such families are obviously usually headed by a male "patriarch," true, but in such situations subordinate men no less than subordinate women are dominated by family leaders regardless of their sex.)  That said, here's how I think it works.

An adult woman might be able to marry who she chooses. The more autonomous she is and/or the more authentically committed to her (mono or poly) marriage the less likely she is to negotiate for separate wealth such as a dowery. Why should she? Even if marriageable women are scare she'll be sharing some portion of her husband's wealth and/or estate.

To the extent parents can negotiate for the marriage of their daughter they can instead extract wealth from the husband and/or his family (never assume men have much more choice of spouse than women under real patriarchy.) Unlike the prospective bride herself, her family is unlikely to share directly in the husband's family's wealth. Consequently they have an incentive to attempt one of at least two major bride-price-capturing strategies. First they can arrange a marriage with another family before their daughter comes of legal age. Second they can agitate for cultural or legal means to control who she marries even after she comes of age. Either way they come out ahead, and therefore they have *incentive* to try to come out ahead, and therefore Grossbard's argument holds.

Most of Grossbard's assumptions depend on circumstances where marriageable women are in demand. I'm... pretty sure the agreeable-for-women conditions Cowen is thinking about depend on situations where women are either in neutral demand or negative demand, as in regions and cultures where dowrys rather than bride prices are required to secure marriage for a daughter.

Point being that both Cowen or Grossbard can be right. It just depends on who gets to make the marriage (individuals or their parents) and which way the money flows.

Final point: in his post Cowen says

Polygamy ends when children cease to be a net economic asset. As society progresses and urbanizes, there are cheaper ways of having sex with multiple women, if that is one's goal.

In light of my discussion, above, Cowen can be even more right when he says the key is the net economic asset "value" of children. When it's profitable for a family to retain control over who a child marries they'll do so. When there is little or no such value you get crap like infanticide and children "apprenticed" off for "service" in sweatshops and domestic servitude.

Dumb question: if the "seed spreading," "naturally polygamous" ideologies forwarded by sociobiologists, evolutionary psychologists, and the editors of Esquire and Details were true then where high bride prices are demanded you'd expect at least some men to respond by marrying multiple partners. And yet...

One explanation is that in most such cultures families control not only who their daughters marry but who their sons do as well. Another would be that our notions of sexual scarcity distort the deeper reality that polygamy is virtually always either an economic or political rather than a sexual arrangement. Brigham Young didn't marry 143 women because he wanted to have sex with them -- many or most had property that accrued to their husbands upon marriage.