The principle of an overarching Court has been on the table, so to speak, for a number of years. Judge Howard Holtzmann and Judge Stephen Schwebel set out proposals for the creation of such a court in 1993, at the Centenary Conference of the LCIA in London. The concept of an International Court to control arbitration is a relic of the view of arbitration as some kind of extension of the state power into private hands, to be given grudgingly, with the state always holding something back. Of course, non-lawyers know very little of law, but one thing they know, which lawyers do not, is that law is not the whole of life. We start from the premise that disputing parties have a right to determine their differences themselves, alone or with help.
Arbitration is that help.
It is not a creation of law, but a private process whose utility is recognised by systems of law, albeit on terms which those legal systems may choose to impose, and which must be respected. The idea of appeal to the Court is already uncomfortable in some respects. An Arbitral Award is a decision made for and, in a sense, by the parties. It is not a decision of a Court of Law, it is their own decision. Of course it is open to the Courts of a State to decide whether or not to enforce that decision, just as it is open to the Courts of a State to decide what other aspects of rights and obligations between parties will be recognised.