If you would not mind i would like to return to the subject of this thread - articles.
The paragraph below compasses three original sentences. As you can see from the bold words the first phrase has a determiner while the second one does not have. If it was vise versa I could think of 2 reasons to explaine this. But it is not. So I would be glad to hear your thoughts.

If within thirty days after the receipt of a party's notification of the appointment of an arbitrator the other party has not notified the first party of the arbitrator he has appointed:
(a) The first party may request the appointing authority previously designated by the parties to appoint the second arbitrator; or
(b) If no such authority has been previously designated by the parties, or if the appointing authority previously designated refuses to act or fails to appoint the arbitrator within thirty days after receipt of a party's request therefor, the first party may request the Secretary-General of the Permanent Court of Arbitration at The Hague to designate the appointing authority.