Well, if I recall correctly, before he got really in to acting he was a very scholarly person for several years, putting off his ambitions while he studied. It could be possible that Arnie actually DOES know something about governing.
Although that waits to be seen...
Besides, was there REALLY any question of Arnie NOT becoming Governor, with all the publicity (and women) in his campaign added to his huge fame I don’t think the other candidates stood a chance.