Polygyny occupies that space in international human rights law, and with pressure to apply it in the same way to Canada's legal interpretations as well. The basis of the argument is that polygyny puts women in a risky situation without equitable marriage rights (Kelly, 2007), even in Canada's more friendly legal structure.
So, what does this have to do with polyamory? Well, the knee-jerk reaction from the rest of the world would be to see the superficial similarities between polygyny and polyamory: multiple partnerships. Though the distinctions are quite limited, with polyamory identifying with a much more egalitarian and equitable gendered framework than polygyny. This goes as far as to even identify critiques of monogamy as having some similar women-repressive characteristics that polygyny has (Kelly, 2007), though to a lesser degree.
So then, if polygyny is on the far end of the misogynistic scale, monogamy somewhere in the middle, and polyamory on the equitibility end, does that mean there's a legitimate human rights argument in favor of state or national-level endorsement of polyamory?
I hate to say this, but I believe the answer is ultimately 'no.'
The human rights angle is informative, but doesn't address root-problems, it just takes a historical and, honestly, a stereotypical sample of the intention behind a relationship form, and attempts to put a human rights value judgement on it. Consider that some polygynous arrangements could be more egalitarian than some monogamous or polyamorous arrangements. There's an individual character of the relationship itself that is lost when assessing at a simply structural level when family is involved.
It's important to allow room for a multitude of configurations, however opening up the law to just simply allow whatever kind of partnership is just as problematic. The issue boils down to this: Policy, group narrative and individual behavior are co-reinforcing. The narrative of monogamy, polyamory, polygyny/polygamy is already present, people are forming their relationships around these structures.
In the case of monogamy it's fairly cut-n-dry, tons of laws and structures in place to support a monogamous couple, and TONS of social, policy, and other resources available to direct the couple towards particular behaviors, ideally behaviors that encourage equity. This is despite being based on an ownership-orientation structure, where the man owns the woman, exampled partially by how the woman takes on the man's surname, a changing custom.
Polyamory is similar in how the internal culture treats it. Polyamory lacks the support of policy and the larger cultural narrative, but it's structural foundation is based on very modern ideas, including human rights equality. In a lot of ways this is why polyamory is able to continue operating, because it's based in modern concepts of relationship polyamory is able to 'blend' with the modern-day norms.
Polygyny, on the other hand, is very strongly rooted in an ownership-orientation structure, and it also lacks the support of the culture at-large, to the point of laws being made to specifically counter it.
Yet we're back to the original problem, how can structure be a factor in relationship equity? Well, it can and it can't. Again, it depends on the individuals. There is, however, a relationship between the larger social structure and policy to help frame individual's relationship to being in relation.
One of the interesting balancing points between human rights and multiculturalism is where belief is differentiated from practice. I.E. Multiculturalism can only be accepted to the point where one person's right to multiculturalism doesn't infringe on another person's right. Things such as safety can interfere in individual's multicultural rights (Kelly, 2007).
This all puts polyamory on a very precarious edge. On one side, polyamory has a strong, and modern, human rights foundation to fall back on, polyamorous individuals have a great many internal resources that have been built from modern ethical frameworks to construct their relationships by. Yet on the other hand, the potential comparison's between polyamory and polygyny make it unavoidable to accuse polyamory as having the same potential issues that polygyny has.
Yet on the other end of the spectrum we have monogamy, which consists of an ownership-oriented foundation, covered by modern ethics.
So what happens now?
References: (Author Note: I kept the references light tonight, law and policy are still fresh turfs for me, so I don't have much to work with)
Kelly, L. (2007). Bringing international human rights law home: An evaluation of Canada’s family law treatment of polygamy.University of Toronto Faculty Law Review, 65(1), 1-38. Retrieved April 4, 2011, from OmniFile Full Text Select database.