There is a myth that computers will always make things better and a great example of this myth in action is voting. While computers are great at adding up numbers they don't know what those numbers mean and the code that adds those numbers can be tampered with. In fact because of the way voting works today it's impossible to track if a vote was properly counted.
When you vote you want to know that your vote was counted correctly. You also want to know that someone elses vote was not counted twice. You need trust and security.
You need the trust and security you get at a bank. When you deposit $1,000 at the bank every dollar is counted. You have basic accounting, receipts and balances that allow both you and the bank to figure out where the money goes. Why is voting any different?
Well, for one you want to be able to vote anonymously. You can't make voting records public because unscrupulous individuals could coerce or intimidate people into voting a certain way. What you want is anonymous but verifiable receipts.
Imagine I go to vote and when I get to the voting booth I take a dollar bill out of my pocket. When I vote I insert the dollar into the voting machine and when I'm done I get my dollar bill back plus a receipt of my vote. It's an ordinary dollar bill, there's nothing special about it. In the voting process the dollar bill and I are similar. We are anonymous and we are unique. Each bill has a unique serial number. Once voting is complete and the votes have been tallied the serial numbers of the bills and the corresponding votes can be released publicly.
Anyone who voted can go lookup their own vote by finding their own serial number. Voting is still anonymous, no one can tell who you voted for but you can verify that your own vote was counted. The bill serial number acts as a unique receipt. Since the bill is difficult to forge it doesn't matter how the actual ballot is done you have a verifiable way to track your own vote. If your vote was counted incorrectly you can bring your bill as proof and correct the mistake. (Of course don't spend that bill until the election is over.) If your vote was never counted the paper receipt plus the bill are proof of the place, location and unique machine used to vote. This can be used to back-track and find faulty machines that issued receipts but didn't actually count votes.
You no longer have to worry about the poor design of voting machines, hanging chads, miscounts, recounts, and widespread election tampering. Everything can be done out in the open. Only with an open process can you have public scrutiny to ensure that everything is just and fair.
What about other people's votes? How can I know that other people are voting only once? Interestingly the answer is non-technical. We can learn a lesson from Iraq that used a similar process in their election: