For example, under Brazilian law a father has to give alimony to the child, even if the mother of the child doesn't want/need the alimony. The reason for that is that the alimony is for the child and it is an irrevocable right the child has.
Now let's assume the couple decides to have the alimony discussions within an arbitration court.
This arbitration court still needs to abide by the law. So, let's say the couple decide that no alimony needs to be paid, it is not lawful, even though it was sanctioned by the arbitrage guy.
My point is that the same set of laws should apply within one country always.