Over at the Bad Idea Blog, "Bad" notes that advocates of same-sex marriage often simply dismiss slippery slope arguments such as the claim that judicial rulings in favour of same-sex marriage would lead to the legal recognition of polygamy.
This is a horrible-result type slippery slope argument against gay marriage ... or it could be framed as a reductio ad absurdum argument against reasoning that is said to support same-sex marriage. But one problem for such slippery slope arguments is that they are sound only if the outcome at the bottom of the slope really is horrible. Similarly, reductio ad absurdum type arguments succeed only if what is entailed by the impugned premises and reasoning really is absurd. However, I see nothing obviously horrible about a society that is prepared to register polygamous marriages (assuming all parties involved are legally competent). Polygamous arrangements are already perfectly legal; they are just not officially "marriages" in most societies. If they were given such legal recognition, I don't see why that is so obviously a horrible outcome.
Similarly, if a legal argument in favour of same-sex marriage also entails that the state should recognise polygamous arrangements as "marriages", I see no evident absurdity.
Hence, the argument simply fails as a rational argument against same-sex marriage; strictly speaking, nothing more need be said.
However, I'll say some more anyway. Nothing above should be taken to suggest that I hold up polygamous marriages as an ideal. It certainly doesn't mean that they should become the norm for everybody to aspire to, as in some religious or cultural traditions. But liberal societies do not require that we all live in a way that is judged to be ideal or that any arrangement that is recognised officially is thereby promoted by the state as a norm for everybody.
At the Volokh Conspiracy, there's a brief attempt by Dale Carpenter to distinguish gay marriage from polygamous marriage. Although "Bad" is impressed by the attempt, I must say that I find it rather flimsy (I must, in fairness, also point out that Carpenter has written at greater length elsewhere, and I encourage interested readers to follow his links).
I don't have time to give my full reasons here, but all the arguments against recognising polygamous marriages strike me as contrived. Perhaps the strongest point against polygamy is that there might be social difficulties if polygamous marriages (in the form of polygyny) became very widespread. But, again, polygyny is already legal, just not officially recognised as "marriage". Nothing in the law prevents me from going off tomorrow to live in orgiastic, but perhaps distracting and exhausting, bliss with my four favourite women (who probably know who they are). What prevents it is that they'd laugh at me if I offered such a suggestion. More generally, what prevents polygyny in Western societies is just that women (far more often than not) don't and won't want it.
We do not usually take official action to discourage something merely because it would cause social problems if "everybody" (or, more accurately, a large fraction of the population) did it. Rather, we assume the reality of social pluralism - that different people are likely to live in accordance with many different systems of values.
If Western states began to recognise polygamous marriages it is doubtful that this would have any great impact at all on (for example) the percentage of polygynous arrangements or the percentage of sexually frustrated men, let alone the percentage who might thereupon become alienated and possibly violent. The fact is that most women would remain just as wary as they are now about entering into long-term polygynous arrangements. While some women probably benefit from polygyny in some circumstances, most Western women would, quite understandably, not be willing to enter into such asymmetrical sexual arrangements at all - and certainly not long-term or without the option of easily leaving and finding alternative partners.
(That said, some women from some cultural traditions, such as the Maasai, may actually prefer to enter into a long-term arrangement where they have female companionship within the arrangement. Such preferences are not out of the question. But if, by chance, a tiny number of such women are to be found in Western societies, why not cater for their preferences? Some value systems may seem strange to most Westerners, but, in the absence of significant harms, that doesn't entail that the state should consider them unwelcome.)
For a different reason, it is weak to claim that it's inexpedient to recognise polygamous marriages because it would require modifying such things as probate law. The modification might not be enormously difficult in principle, and the fact is that such problems could already arise in circumstances where, for example, a participant in some kind of legal (but unofficial) polyamorous arrangement dies intestate. If the opportuntity were taken to tidy this up, it might actually yield intuitively fairer results.
Polygamous marriages are not the ideal, but there may not be a single ideal. Societies where polygyny is held out as the norm are thereby likely to inherit some problems, but I am not going to condemn polygamists' view of the good for that reason. Even if I were inclined to do so, based on personal moral beliefs or social concerns, I don’t think that the state should be doing so in a liberal society. So, if we are going to give state recognition to marriage at all, why not to polygamous marriages as well (provided all involved are competent adults to the same extent as is required for "ordinary" marriage)?
In all, I consider this particular argument against same-sex marriage weak, because what is (supposedly) lying at the bottom of the slope does not seem all that horrible. If we end up officially accepting polygamous marriages, so be it. I believe that people who run this argument against same-sex marriage are essentially appealing to irrational fear and prejudice.
But there's another possibility. Perhaps what I've written so far is wrong, and some compelling public-policy reason can be identified for not recognising polygamous marriages in particular. This would, in other words, be some great problem if polygamous marriages were recognised by the state. In that case, the result is horrible after all - but the slope is not slippery. It's not slippery because, on those facts, a principled distinction can be made between recognising same-sex relationships as marriages and recognising polygamous arrangements as marriages.
All in all, this policy issue about same-sex marriage is not a case where you can, with success, simultaneously argue that the slope downhill is slippery and that the outcome at the bottom of the slope is (on appeal to reason, rather than mere prejudice) horrible.
That, of course, is the common problem with horrible-result arguments. It is very rare that such an argument can succeed by showing simultaneously that the slope is slippery and that the result is horrible. Generally, the more horrible the result the less slippery the slope.
All that said, I have repeatedly argued elsewhere that the optimal solution is not the official recognition of many different kinds of relationships as marriages.
Rather, we should simply continue to allow individuals to enter into whatever sexual, familial, and domestic relationships they want, with whatever support they can muster from their cultural and religious communities, their families, and their friends; at the same time, the state should cease recognising relationships that meet some prescribed template as being, officially, "marriages" (and so registrable as such by some public agency).
On that scenario, anyone - gay or straight, monogamous or polygamous, or whatever - can have a marriage ceremony, call themself "married", and have the "marriage" conducted and recorded by the religious or other organisation of their choice. Government forms would no longer ask people whether they are married, and the state would be neutral about people's personal relationships. People would remain free to enter into contracts, trust deeds, etc., to determine the distribution of property on breakdown of a relationship. Courts and legislatures could continue to develop principles to deal with unconscionable agreements or to divide assets in the absence of agreement (in the absence of appropriate legislation, courts began to develop such principles some decades ago for de facto couples, essentially expanding the operation of the law of trusts to fill what was then a serious gap).
I'll say once more, for the record, that I do favour political policies to introduce provision for same-sex marriage, but only as a realistic compromise in current circumstances, not as the optimal long-term solution in a liberal society.