Pay Las Vegas casinos a big wad of money to create a truly foolproof voting system using other casinos/groups to transparently verify that the system is legit. Then let the casinos take bets on who's going to win various elections.
Seriously. What other single group of people has more experience in making and administering cheat-resistant systems? Plus if you make the system transparent you wouldn't have any magic black boxes that could be set to do bad things (e.g. miscount votes) you'd only be using their expertise in foiling cheaters.