What's wrong with electronic ballots? If we can have a secure and audit-able banking system (and every other aspect of our lifes), surely we can have the same for voting?
There's one major requirement in voting systems that throws a huge wrench in everything, anonymity. In order to prevent vote buying and coercion voters can't be tied to specific votes. So any system that allows a person to check that their vote got counted for their candidate isn't workable because that violates the anonymity requirement.
There's a million reasons that votes change as they're counted and recounted. For one in some states absentee ballots can be postmarked up to the day of the election so they can trickle in for a while after the day of. Another is machine breakdowns and just mistakes as the complete numbers are gathered.
There are several other major problems with their system [0], but I think they should at least get credit for their approach.
First of all, you can't observe the counting project, and now if somebody want to mess with the results, it becomes super easy to do so.
Electronic voting is a great opportunity for dictatorship.
And we know they do, because it's trivial to observe. Without paper it would be totally opaque, you would just have a raw number and nothing else.
The US requires that once you leave the polling station you must not be able to prove to anyone how you voted.