I am not aware of any pre-employment arbitration agreement which specifies a specific arbitrator. Most specify that a member of a specific group or association must be selected. I doubt that most employers actually know much about the individual arbitrator who is selected (ahead of the selection).
"Arbitrator" here means "the organization the company uses for arbitration", which'll have a set of training standards etc. they tend to have. You shouldn't get wildly different results with different individuals within a one.
I think you'd be surprised at how different individual arbitrators can be. Judges appointed by the same government and operating within the same laws can also vary quite widely.
