If the plaintiff fails to show up and has given no valid reason for his or her absence, oftentimes the arbitrator will recommend the case be dismissed. If the defendant filed a counterclaim against this plaintiff, the arbitrator will likely hear the counterclaim in the plaintiff's absence and make a decision on the counterclaim based on the case presented by the defendant.
If the defendant doesn't show up, and no valid reason is given for his/her absence, the arbitrator will hear the plaintiff's claim and make a decision based on the plaintiff's evidence in the defendant's absence. If there was a counterclaim by the defendant, but the defendant wasn't there to present that case, the counterclaim will likely be dismissed.