Immediately after the last day is fixed for the withdrawal of nominated candidates under section 413 of this subchapter, the Supervisor of Elections shall fix a day for the casting of lots, in such manner as he prescribes, for the position of the names upon the official election ballot of all candidates nominated for the election by the vote of party electors at the immediately preceding primary, and nominated for election by nomination papers. The Supervisor of Elections shall give at least two days' notice of such date by publication in the local newspapers circulating in the Virgin Islands or district, as the case may be. Each candidate may appear in person, or by an agent duly authorized by letter of attorney, signed and acknowledged by an officer empowered to take acknowledgments. If any candidate is not present in person or by representative at the time of the casting of lots, the Supervisor of Elections or his designee shall draw for such candidate. After the lots are cast, the Supervisor of Elections shall establish accordingly the order in which the names of such candidates are to appear on the official election ballot.