Utah Const. art. IV, § 8

[Election to be by secret ballot.] (1) All elections, including elections under state or federal law for public office, on an initiative or referendum, or to designate or authorize employee representation or individual representation, shall be by secret ballot. (2) Nothing in this section may be construed to prevent the use of any machine or mechanical contrivance for the purpose of receiving and registering the votes cast at any election, as long as secrecy in voting is preserved.