All contested elections for electors shall be determined by a joint vote of both houses of the general assembly. The joint meeting of the two houses deciding on such elections shall be held in the hall of the house of representatives, and the president of the senate shall preside. If any person contests the election of an elector, he shall present a petition to the general assembly, setting forth the points on which he will contest the same and the facts which he will prove in support of these points, and shall pray for leave to produce his proof; and a vote shall be taken in the house, by yeas and nays, whether the prayer shall be granted. If the majority of the whole number of votes of both houses shall be in the affirmative, they shall appoint a joint committee to take the testimony on the part of the petitioner, and also on the part of the person whose place is contested, with the power to send for witnesses, issue warrants, under the hand of the chairman, to any judge or associate circuit judge, and to take the depositions of witnesses at such time and place as the warrant shall direct, which warrant shall mention the points to which the testimony is to be taken. Reasonable notice shall be given by the party in whose favor the deposition shall be allowed, to the opposite party, of the time and place of taking same; and the judge or associate circuit judge shall proceed in all things, in procuring the attendance of witnesses, and in taking and certifying the testimony, as is directed herein.