The ruling is in. The prohibition has been upheld as a reduction of harm measure against the changes of impingement on religious freedom. The fundamental basis for the ruling seems to be that the Judge found polygamy to be harmful in and of itself and much of the ruling is based on that finding of fact.
So what does this mean for Brown? Not a whole lot really. While international law has been gaining some influence on American courts, it is not a central part of the analysis. The finding of fact on polygamy might be something the courts cite to because it is an issue of fact and not law, but because it is an issue of fact the finding will not hold a position of greater validity in the American court system than any other will researched finding by a respected investigator. It is, none the less, disheartening to have this finding in the background of any future polyamory cases.
The other thing is that this case is something that couldn’t happen under US law, it would fail the standing test that is currently at issue in the Brown case, not that this is a reason it can be looked at, but it does make it harder for American courts to understand and inapplicable to the current issues in the Brown case.
The part of the case most analogous to the Laurance issue in Brown is Section C on Freedom of Association (Yes, this is in the American Constitution too, but the legal systems have evolved and treat these very differently). The arguments are not directly like the privacy based arguments from Laurance, but are similar to the arguments likely to be made in a polyamory case. The Judge found that association did not protect the activities associated with marriage. I don’t know enough about Canadian law to evaluate this section, but it seems like protection simply was not extended to marriage like activities.
Another interesting section is Section D which is about other legal principals such as arbitrariness and consent that do not seem that differently applied between the legal systems. They are all struck down using the finding of fact, that polygamous marriages are inherently harmful and cause social harm, as the sword.
So this reference case is not good for polyamorous people living the US, but its impact might be limited because the case as a whole is a poor analogy to US law and the