The fourth Friday in May of the election year, the Supervisor of Elections shall fix a day for the casting of lots, in such a manner as may be prescribed by the Supervisor, for the position of names on the official primary ballots. The Supervisor of Elections shall give at least two days' notice of such date, to all candidates whose petitions have been received and filed in his office, by mail to each of them and by publication in the local newspapers circulating in the Virgin Islands or district, as the case may be. All candidates may appear in person, or by 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 shall appoint a person to represent such absentee. After the lots are cast, the Supervisor of Elections shall establish accordingly the order in which the names of such candidates are to appear upon the official primary ballots.