The legislative body of each city and town shall appoint a bipartisan canvassing authority of three (3) qualified electors of the city or town, not more than two (2) of whom shall belong to the same political party, and may appoint two (2) alternate members, not more than one of whom shall belong to the same political party. At any meeting of the canvassing authority at which a member is to be absent, the member may request that an alternate replace him or her for that meeting; provided, that the alternate member must be of the same political party as the member. The mayor or the president of the town council shall nominate the members of the canvassing authority from lists of party voters submitted by the respective chairpersons of the city or town political committee, which lists shall contain the names of five (5) times the number of persons to be appointed. If the legislative body refuses to approve the nomination of any person to the canvassing authority, the mayor or the president shall submit to the legislative body another person named on one of the lists, and so on until a person is appointed. If the chairperson of the city or town committee of a political party entitled to an appointment fails or refuses to submit a list, the mayor or the president shall nominate any party voter of the political party entitled to the appointment.