(a) Candidates for the various political parties for party offices who receive a plurality of the votes of the party electors at a primary election shall be declared elected.
(b) In the case of a tie vote for any party office, the candidates receiving the tie vote shall cast lots before the Supervisor of Elections or his deputy at a time and place to be fixed by the Supervisor of Elections and the one to whom the lot shall fall shall be declared elected. If any candidate receiving a tie vote fails to appear at the time and place fixed by the Supervisor of Elections the Supervisor of Elections or his deputy, as the case may be, shall cast lots for him. For the purpose of casting lots, any candidate may appear in person, or by proxy appointed in writing.