If we look at security critical systems, say banking, electronic gambling, a great deal of care is put into making those machines secure, and still problems occur. I consider electing the leader of the free world to be a more critical question than who wins the lottery.
With the paper-based system you can see the ballots being marked, you can see them going into a ballot box, if you have good laws you can go watch them count the ballots, and with electronic voting all of that stuff is hidden inside the machines.