I'm coming around to the idea that polyamory may not be as euvoluntary as I'd previously argued. Short version: a polyamorous marriage may be fine, but I have to agree that as an institution, it has some pretty serious predicted shortcomings.
So here's the question: does the logic of prohibition apply to plural marriage? Will desperate consumers resort to black market harems to secure illicit booty? Would a legal regime in which abused plural marriage spouses were free to contact law enforcement agents for assistance without fear of reprisal reduce the severity and frequency of bride trafficking?
I'm not familiar enough with the law enforcement statistics to judge. Swinging is legal, so is cohabitation. A married couple can have a "roommate" without attracting attention. Open marriages are fine. People are already pretty much at liberty to set the terms of their domestic arrangements, so it's difficult to say that there's much of a thwarted market the way there is for cocaine or extended-capacity AK-47 magazines. It's possible that whatever downsides that accompany polygamous institutional arrangements are already being felt. If so, to consider a legal regime means to consider what the potential upsides would be.
I'm not sure what they'd be though. Inheritance? Estate execution? There's not much common law guidance there other than what already exists for business partnerships. Seems kind of a slender reed.
At any rate, I think one of the problems with discussions of law and relationships is one side is talking about private costs and benefits, while the other is talking about public costs and benefits. Is it a self-interest debate or is it an institutional debate? And which of those should provide a basis for a compelling state interest?