The court for the trial of contested county elections shall consist of one member named by the contestant and one member named by the incumbent. If the incumbent fails to name a member, the chief judge of the judicial district shall be notified of the failure to appoint. The chief judge shall designate the second member within one week after the chief judge is notified. These two members shall meet within three days and select a third member to serve as the presiding member of the court. If they cannot agree on the third member of the court within three days after their initial meeting, the chief judge of the judicial district shall be notified of the failure to agree. The chief judge shall designate the presiding member within one week after the chief judge is notified.