I am sorry for this late reply to the many interesting posts on polygamy. I will not be able to consider all the issues raised, but I discuss a few. I come back to the comments on crime next week.
Someone asked about how polygamy would affect the incentives of men to invest in more skills, etc in order to be more competitive in marriage markets? We do know from historical data that men tend to marry later in polygynous societies in order to have enough income and wealth to be sufficiently attractive as mates. However, if sharing of resources in a marriage is determined by supply and demand considerations, one can show that the investments in skills and other ways to be more attractive are efficient (see the discussion in the chapter on marriage in the book, Social Economics, by Kevin M. Murphy and me). However, if sharing is based on rigid rules, such as 50/50 split, investments in skills may be either excessive or insufficient from an efficiency perspective.
Clearly, polygyny has sometimes been encouraged when there is a shortage of men, as when many men have been killed in war. As William Julius Wilson and others have emphasized, there is now a significant shortage of eligible men in black communities. Perhaps that would lead to a little polygyny if it were allowed, but as I said in my post, polygyny is quite rare in modern societies even when permitted. I explained this by a substitution of quality of children for quantity. I agree with one comment that it also involves a substitution of one higher educated wife for two or more less educated ones.
I do not believe there is much of a biological argument against polygyny. For most non-human species are polygynous, not monogamous. I believe polygyny has also been more common among mammals than monogamy. Probably, a majority of humans in the more distant past also lived in polygamous, not monogamous, societies. So if anything, monogamy has evolved due to culture and against biology.
Do girls need protection against polygamy? Not if it were openly allowed rather than an illegal activity in some remote rural area of Utah. I repeat what I said in my post: I have considerably more confidence than some of the posters that young women can make at least as considered decisions with respect to marriage as young men. If, however, there is a belief that young girls will be taken advantage of, have a law that raises the minimum age before girls can enter into polygynous marriages.
Some completely erroneous statements were made in one of the comments about the relative commitment to marriage of men and women. These were well answered by other posters, so I will only add that I assume this view also implies that women are less interested in having custody of children than men?
My comments on gays having children were made only to point out how many marital practices that were forbidden in the past are now allowed. Perhaps I am wrong in my view that there tends to be negative effects on children raised by gays. I do not strongly hold this view, and look forward to the time when we have more convincing evidence, one way or the other.