Take a look at this short and sweet TED talk by David Bismark about a new system that provides for electronic voting. It provides encrypted safety for voters, transparent results and yet you can go to a terminal and see your own vote count.
(Electronic voting TED talk by David Bismark)
My first exposure to the idea that electronic voting could work is in The Shockwave Rider, a 1975 novel by John Brunner.
From 0700 local until 1900 every veephone on the continent would display, over and over, two propositions, accompanied by a spoken version for the benefit of the illiterate. Most would be in English, but some would be in Spanish, some in Amerind languages, some in Chinese ... the proportions being based on the latest continental census. After each repetition would follow a pause, during which any adult could punch into the phone his or her code, followed by a "yes" or "no."
(Read more about Brunner's proposal for electronic voting)
Brunner did not invent the concept; as far as I know, Buckminster Fuller was probably first in 1971 to write about "electrified voting".