Robert Frank discussed polygamy from an economist's viewpoint in the March 15 edition of The New York Times; just like its editors a few years back, Franck is ignoring the moose in the room.
This is occasioned by the premier of Big Love on HBO last week - the fictional story of a polygamist family trying to go mainstream in contemporary Utah.
Frank asserts that since women voluntarily enter into polygamous relationships, the criteria for judging the merits of this institution should be whether or not they do "unacceptable harm to others".
This is a problematic assertion because one of the women in a polygamous relationship did not voluntarily enter into a polygamous relationship at all. The (chronologically) first wife entered into a monogamous relationship, the terms of which were later changed.
This is a hold up problem - the idea that once a contract for a bundle of goods is entered into, that it may be advantageous to one party to change the contract, and that the second party (though hurt) may agree for the sake of maintaining as much of the contract as possible.
Thus, one could argue that Frank is only correct if the husband and all the (potential) wives marry simultaneously. Clearly the world doesn't usually work this way, so I don't think this is any more than an intellectual curiousity. This suggests that the husband does harm to the first wife in a polgyamous relationship, and therefore we have grounds for making this illegal.
You could also argue that the first wife knew what she was getting into. No doubt this is sometimes true (if not, we're back to the hold-up situation). Options theory is informative about the effects in this case. The first wife is in the position of a writer of an option held by the husband (the writer has the obligation to fulfill the option exercised by someone else - in this case the first wife is expected to stay in the marriage when wife #2 shows up). Again, this works, provided that wife #2 is on the scene initially. If not, she is a third party who has changed the value of the option to the husband and first wife. In and of itself this is not illegal, but it is generally held to be illegal if you not only change the value of someone else's option but stand to gain by doing so. So in this case, the later wives are guilty of causing unacceptable harm.
Of course, the Coase Theorem now applies: if harmed the first wife should be able to correct the inefficiency resulting from these externalities. Anecdotally this is confirmed in practice, and is on display in Big Love where the first wife is pejoratively called "boss wife" for fairly clear reasons (I can also personally confirm having seen boss wives in action around my town).
If the inefficiency is completely and voluntarily corrected, I think we may be back to no harm no foul. Personally, I have my doubts that this is the case, but the evidence is circumstantial so bear with me while I speculate. Within the FLDS polygamist sect, my understanding is that only men are admitted to heaven; women enter heaven only when invited by men they were sealed to as a mortal (Mormons may object to my use of the term sealed, but FLDS members use it in much the same way). Could this belief influence the willingness of a first wife to have the value of her marriage contract reduced? My guess is that it could. In support, we have the case of polygamy in Moslem cultures where the cooperation of first wives is ensured by the removal of their rights outside the family. Again, it seems that this might make them more amenable to reduction in the value of their marriage contract.
In sum, I think Frank has missed an important economic argument against polygamy, and hasn't even mentioned the evidence that might lead in this direction.
FWIW: The wide open question about all this is why the group in America most associated with polygamy (the FLDS sect) is also heavily engaged in a variety of criminal activities (see my Polgamy - FLDS subject category for details).
Disclaimer: I get some flack about polygamy posts, so let me note once again that I don't have a dog in this fight: I'm not LDS, FLDS, pro-polygamy, or anti-polygamy ... I just happen to live in an area where I have more occasions to think about the issues than the average blogger.