How are arbitrators selected? The employer and union must agree upon a process to select an arbitrator. The American Arbitration Association (AAA) or Federal Mediation and Conciliation Service (FMCS) supplies a list of five potential arbitrators. The employer and union must put all the names in a hat and take turns pulling a name, and the last one is the arbitrator. The employer and union must agree in advance of the first meeting on who will be the arbitrator