This third party arbitrator’s decision... if it is not liked by one party. Wouldn’t that party demand an arbitrator on the decision1? But then couldn’t decision

This third party arbitrator’s decision... if it is not liked by one party. Wouldn’t that party demand an arbitrator on the decision1? But then couldn’t decision2 be demanded to be arbitrated by the other party. And then. And then... it doesn’t seem to stop? In other words it seems you would need some kind of judicial process to keep in check the arbitrators. Which then sounds just like regular money, where you can usually arbitrate many times? I’m also in the grandparent’s boat and I just want to get another view on this.