CA Civ Proc Code Section 1297.118

The superior court, in appointing an arbitrator, shall have due regard to all of the following:

(a)

Any qualifications required of the arbitrator by the agreement of the parties.

(b)

Other considerations as are likely to secure the appointment of an independent and impartial arbitrator.

(c)

In the case of a sole or third arbitrator, the advisability of appointing an arbitrator of a nationality other than those of the parties.