The parties file a written consent form that submits the case to binding arbitration. After completing and signing the arbitration agreement, the parties must submit the document to the arbitrator or arbitration firm that they've selected. 4.If mediation doesn't work, the employee might agree to try arbitration, or they might file a lawsuit. On appeal from the Superior Court of New Jersey, Law. Division, Middlesex County, Docket No. L-1085-23. I'm starting a new job soon and one of the pieces of paperwork they want me to fill out is an arbitration agreement.