[maccam94]

It is fundamentally impossible to have secret ballots[1] in a digital system along with provable integrity. Secret ballots are necessary to prevent vote buying, intimidation, and coercion. If no one can prove which voter submitted which ballot, nor what choices a voter indicated, the voter is free to choose without risk of repercussions. The breakdown of any digital voting system is always with verification.

With paper, the voter can see that their ballot is securely stored under the supervision of the election operators, and they can see that representatives from multiple parties watch the movement and counting of the ballots.

In contrast, with a digital system it is impossible to verify that your ballot was delivered with the choices you intended without also being able to show that proof to anyone else. It is important that the voter is unable to show proof of their vote for the reasons mentioned above. Unlike a paper-based process, you cannot directly observe the functioning of an electronic circuit, the transmission of data over cables, or the storage of bytes in memory, and neither can anyone else trying to verify the integrity of the process. You'll never know if someone has replaced any of the hardware or software components with malicious versions designed to fool voters and rig elections.

1: https://en.wikipedia.org/wiki/Secret_ballot

[ShorsHammer]

I can prove the existence of X with zero-knowledge proofs without exposing X. Obviously there's more from there for elections but the cryptographic groundwork certainly exists.

[jobigoud]

But unlike the paper mechanism, the average person, nor the experts for that matter, can verify the correct and uncompromised implementation of the zero knowledge algorithm. You trade off the understandability and verifiability of the scheme.