But they don't need to understand the mathematical details of the cryptographic protocol (do they?), which seemed to be what you were implying. It seems to me the details could easily be abstracted away into a sequence of idiot-proof steps, but I don't know much of anything about public voting systems.

Edit: I'm not sure why I'm getting downvoted - am I misinterpreting what specialist is saying? For another example, look at HTTPS - it secures your communication without any need for knowledge of how it's doing so, you just need to know that if you see the green lock icon you're "safe" (though I'm aware of all the usability issues, like how everyone just ignores warning messages when something goes wrong). Is there something fundamentally different about public voting systems in this regard?