Mediation and Arbitration get their effect and authority, not from man-made laws (although most jurisdictions do have arbitration laws), but from agreement by the participants. Most modern civilizations uphold the right to contract. If two parties agree to something (not illegal or against "public policy"), that agreement can be enforced. If the contracted agreement is for any dispute to be heard by eMediate (a private arbitrator), then the parties are required to do as agreed.
The Federal Arbitration Act, of which the Convention on the Recognition and Enforcement of Foreign Arbitral Awards is a part, establishes a strong federal policy in favor of arbitration.... Moreover, the liberal federal policy favoring arbitration agreements is essentially a policy guaranteeing the enforcement of private contractual arrangements. However, arbitration may not be compelled in the absence of an agreement to arbitrate. China Minmetals Materials Imp. & Exp. Co., Ltd. v. Chi Mei Corp., 334 F.3d 274 (3d Cir. N.J. 2003)