Lawrence vs. Polygamy.
Despite several fine efforts, so far no one has managed to show there is a way polygamy can be kept illegal under the core reasoning of Lawrence.
I especially liked Peter Sean Bradley's "sui generis" angle, both here and at his blog. Tom Fitzpatrick's "2 ain't 3" unprincipled principle has some potential, too.
But the best shots were derived from the actual language of the opinion: using Lawrence's equally warm and fuzzy language about the state interest in regulating marriage.
But that's not really the problem. The question isn't so much whether the state has to recognize polygamy as an officially valid marriage and so forth. The question after Lawrence is on what principled, rational, coherent basis can the state jail consenting adults who are in a polygamous relationship? Or, as others have noted, any form of consensual adult relationships?
[As noted below, our Weimar elite are working on the kid angle, but that will still take some time....]
Social science arguments attempting to distinguish polygamy won't work either. After all, many, if not most, human cultures have a history of tolerated polygamy. Islam still permits it. Given time, perhaps the suddenly-authoritative European Court of Human Rights will see its cultural rightness.
Actually, we do permit a form of polygamy. All fifty states recognize a mostly-unregulated form of serial polygamy: It's called no-fault divorce and remarriage. It frequently wreaks havoc on children and society, but so what? Further, if you ever stumble across the renegade Mormon polygamists or their literature, you quickly notice that they claim their marital arrangements are more stable than the monogamous norm, and their kids turn out better, statistically speaking. In a legal battlefield involving duelling experts, I somehow doubt that polygamists would lack for capable social science champions. I wouldn't want to engage in that fight.
Sorry, but I have to declare that, so far, the contest has no winner. Submissions are still welcome, however.