In 2003, Thomas Carbonneau wrote that "freedom of contract . . . Is at the very core of how the law regulates arbitration," and he referred to this as "Contract's Empire." I think Carbonneau is right and that, if anything, arbitration law has moved even further since then in the direction of contract.
Susanna Chehata, Arbitrators' Neutrality in the United Kingdom and the United States, 8 Y.B. Arb. & Mediation 234 (2016).