Tex. Lab. Code § 410.106
Current with legislation from the 2023 Regular and Special Sessions signed by the Governor as of November 21, 2023.
The division shall assign the arbitrator for a particular case by selecting the next name after the previous case's selection in consecutive order. The division may not change the order of names once the order is established under this subchapter, except that once each arbitrator on the list has been assigned to a case, the names shall be randomly reordered.
Tex. Lab. Code § 410.106