Texas Civil Practice and Remedies Code - CIV PRAC & REM § 172.053. Appointment of Arbitration Tribunal

(a) Subject to Sections 172.054(b), (c), and (d) and Section 172.055, the parties may agree on a procedure for appointing the arbitration tribunal.

(b) If an agreement is not made under Subsection (a), in an arbitration with three arbitrators and two parties, each party shall appoint one arbitrator, and the two appointed arbitrators shall appoint the third arbitrator.