Electronic systems introduce single-points-of-failure into the voting process - figure out a way to compromise the machines / vote collection process, and you c

Electronic systems introduce single-points-of-failure into the voting process - figure out a way to compromise the machines / vote collection process, and you can steal the election. Doing the same thing with a manual system requires cheating on a massive scale, which is pretty much impossible to do discretely, making it much safer.