Hard headed they may be, but certainly no other race upon Middle Earth looks out for their own self-interest more than they do. I cannot see how they would be careless with something as important as that.
Dwarves do not want anyone in office who would meddle with their personal affairs or impose regulations on thier precious mountains.
Orcs on the other hand are mindless, drooling fools whose brains would indeed be challenged by a butterfly ballot.
24th Century Dwarves?