At Volokh, Dale Carpenter offers what seem like some some very weak potential arguments for drawing the line at gay marriage, but not polygamy.
*There is nothing in principle that necessarily leads from the recognition of a new type of monogamous union (same-sex unions) to the recognition of polygamous unions. Consider the recognition of inter-racial marriage (a type of monogamous union), which reversed long-standing legal bans on miscegenation and departed from deep cultural disapproval of it dating to colonial times and before. Many warned that reversing miscegenation bans would lead to polygamy, but it did not. To the objection that dyadic inter-racial unions would lead to polygamy, the proper response then was, "Why would it?" One response to the fear that dyadic same-sex unions will lead to a polygamy slippery now is, "Why would it?" Opening marriage to one change because the change seems justified does not mean that opening marriage to every change is justified. Every proposal for reform rises or falls on its own merits. Gay marriage advocates have made extensive (and contested) arguments about why it would benefit individuals and society. It is up to polygamy advocates to do the same.
The ban on gay marriage is sustained not by solemn policy arguments, since there is no actual hard evidence on either side. It's a social taboo that rests on Burkean principles: no society we know of has ever had gay marriage, which maybe ought to tell us something. The legal ban on interracial marriage was a local phenomenon in the South, and the laws were invalidated by a court with a northern majority. Once you have established that society's ideas about what constitutes a valid marriage are not a relevant consideration, I find it hard to see how you can forbid a marriage just because one of the partners happens to also be married to someone else.
*From a Burkean/Hayekian perspective, it's relevant that polygamy has been historically tried and rejected in many human societies. We do not write on a blank slate when it comes to polygamy. Lessons have been learned from this experience and those lessons have led us away from polygamy in the West, in part because polygamy as practiced has been seen as inconsistent with liberal values, individualism, and sex equality. SSM has not been tried and rejected and is not inconsistent with, indeed arises from, Western values of liberalism, individualism, and sex equality. While the burden is on gay marriage advocates to show why we should try it, I think actual historical experience with polygamy suggests that the burden on polygamy advocates is much heavier.
This seems back assward. The fact that no society we know of has ever had gay marriage is not a Burkean argument for it. The law of averages being what it is, we are probably not the first culture to ever think of the idea. So if it isn't around, this suggests that societies which tried it either didn't survive, or abandoned the practice.
*Plural unions have historically most often taken the form of one man having many wives. It seems likely in practice it would take that form in the future. This raises many concerns different from those raised by same-sex marriage, including the greater potential for abuse of women and children. These same concerns do not arise with SSM, which should improve the lot of women and children in gay families (if SSM advocates are right about the benefits, a contestable but separate point).
Huh? How does having more than one wife make a guy more likely to beat his kids? To be sure, polygamy tends to be embedded in societies that tolerate more wife beating. But the polygamy is not the cause of the beating. To make this assertion stick, you'd have to have some evidence that abusive husbands are more likely than others to take more than one wife.
On first glance, the argument seems kind of plausible: husbands who come from cultures that tolerate spousal abuse will be more likely to engage in polygamous marriage. But think about this. The women in abusive marriages to those men are almost certainly going to be from the same culture, the children of conservative parents. They wouldn't be allowed to marry outsiders anyway; plural or single, they'll end up wed to someone who might have been raised to think its okay to slap your wife around once in a while.
*Polygamy will likely mean that marital opportunities will diminish for some men, since a few men who are very wealthy or otherwise attractive as mates will have many wives. This constricts the marriage market for less desirable men, which leaves some with no mates at all or delays their marriages as compared to their opportunities in a non-polygamous society. And unmarried men present all kinds of difficulties for societies. By contrast, SSM will mean that meaningful marital opportunities will be available for gay persons. More people will be married. Thus, SSM expands marriage opportunities while polygamy contracts them.
When opponents of gay marriage argued that marriage should be kept for men and women because it was fundamentally about reproduction, opponents said "Bosh! If that's so, how come we allow infertile people to marry?" This argument merits the same response. If it's so unfair that some men will be left without wives, how come we don't force women to marry them? Because that's an outrageous violation of human liberty, that's why. How much better is it to force women to choose between remaining single, or marrying their second (or third, or nineteenth) choice husband, so that said husband may have all the benefits of married life?
It is not possible to increase, on net, the number of marriages in the country in this way; it is capped at the number of women. Polygamous marriage of the type Carpenter describes contracts the marriage opportunities for some men, while expanding them for other men and most women. Indeed, mathematically, the number of marriage opportunities almost certainly expands under this system, since it puts married people back on the dating market.
Polygamy might decrease the number of married people. On the other hand, it might also decrease the number of single people, since a gender imbalance in the numbers of even marginally tolerable mates will result in some people being forced to remain single. Since my understanding is that men die younger and are more likely to be severely cognitively disabled, this probably relieves a burden on women.
*With polygamy, many basic rules of marriage will have to be changed. For example: if the husband dies intestate, who inherits? How are death benefits split? How are child custody disputes decided if a partner wants to divorce the group? If the husband exits, do the wives remain married to each other? On and on. We could craft answers to these questions, but it will involve a dramatic retooling of marriage as a two-person institution. None of these issues arise with SSM; aside from a few technical matters, the marriage rules remain the same. As a legal matter, SSM involves changes in the wording of statutes that specify “husbands” and “wives” and little more. The basic legal design of marriage as a dyadic institution, embedded in literally hundreds of ways in state and federal law, remains untouched.
I'm no lawyer, so I'm probably missing something important here. But the question of what to do if he dies intestate seems obvious: split the spousal share among the wives, and the children's share among the children. In the case of the polygamous marriages discussed above, the question is easy; the husband is married to each of the wives individually. In the case of more complicated marriages, presumably the marriage ends if all parties want it to, and goes on if some want to stay, with a division of marital assets along basically the same lines we use now. I think the hardest question is what to do with children who may have multiple fathers, but of course, genetic paternity can always be established, or joint child support requirements. These are issues that need to be settled, but they don't seem like things that can't be settled.
Perhaps none of this is conclusive against polygamy nor do I offer it as such. I am sure polygamy advocates have responses to these and other concerns about it. But I do think it suggests that SSM and polygamy present quite different questions of history, experience, logic, and public policy such that we are entitled to treat them as separate issues. We may, despite the concerns and the historical trend against polygamy, one day accept it. But the debate about accepting it will not, I think, turn on whether we have first accepted gay marriage.
Ultimately, I think the gay marriage debate made us ask "What is marriage for?" And the answer we came up with is "Dunno, whatever you want, I guess." Having said that, I don't really see grounds on which we can ultimately deny polygamous
Let me be clear that this is not some backdoor argument against gay marriage. I frankly don't see why legal polygamy should be any worse than gay marriage. Which is good, because I'm pretty sure we'll see it within the next few decades.