In Burress v. John Deere Constr. & Forestry Co., Judge Wilson ruled in the matter of a dispute subject to arbitration that the arbitrator would get to decide which state's law applies and where the arbitration would be held.
I'm not sure about that last part - where the arbitration is held could have osme effect on where subsequent court action to enforce or overturn the award has to be brought. 9 U.S.C. 9 ("If no court is specified in the agreement of the parties, then such application may be made to the United States court in and for the district within which such award was made."). Does the arbitrator get to decide where his award will be reviewed? Perhaps so.