This is placing too much trust in what is incomprehensible mathematics for 99.999% of the population. Even for those who understand it, they won't have any convincing way of being assured that 1) the maths is perfect and there are no flaws and 2) the voting technology in use is perfectly implemented.
On the other hand, the 'nineteenth century technology' of secret ballots is both obvious and simple. It's a shame that people like Vitalik are so dismissive of it.