A student in my Philosophy and Public Issues class is writing her research paper on the moral status of polygamy. She and I were chatting yesterday about arguments for the conclusion that it's immoral, but these tend to be utilitarian sorts of reasons about the parties involved experiencing psychological or financial distress. Of course, we can't expect these sorts of consequences in all cases of polygamy. So there are limits to this kind of line against polygamy. There are other less plausible reasons against polygamy like that it undermines "family values."
Interestingly, many of the arguments for same-sex marriage can be applied to debates over polygamy. If one accepts that each of us should be able to marry whomever we see fit, then it's an easy extension to include marrying more than one person whom we see fit. Of course, one can stipulate that marriage is between only two individuals. But this is akin to insisting that marriage is between a man and a woman. And many people find this sort of "argument" outright ridiculous.
I'm beginning to think that the sorts of arguments that you might have for thinking same-sex marriage is morally permissible can be straightforwardly extended to support polygamy. In addition, the arguments you might have against same-sex marriage can be rephrased in an attempt to undermine polygamy. But, as we discussed in class, the philosophical arguments against same-sex marriage seem to be uniformly unconvincing.
Should we conclude that polygamy is morally permissible?
* If you're interested in reading more on things related to this discussion, the SEP has a nice entry on marriage and domestic partnership.