When any contest shall have been commenced under the provisions of this article for any of the officers mentioned in Section 17-16-65, it shall be the duty of the Legislature, in joint convention, to elect by ballot three senators and five representatives, who shall act as a commission to take the testimony to be submitted on the contest. Every member of the joint convention, at such time, as may be fixed by resolution of the two houses, shall vote for two senators and three representatives as members of the commission, and the three senators and five representatives who receive the highest number of votes shall be declared elected commissioners.