In secure e-voting, what three ways could a dishonest voter "cheat," and why are they hard to catch?

A voter could submit an invalid sum (vote for more than one option), cast an invalid non-binary value, or copy another voter's encrypted ballot — all while every ballot stays secret.

Electronic voting has a fundamental tension: votes must be secret, yet the system must still be verifiably correct. That secrecy is exactly what a cheater hides behind. The three classic cheats:

1. Invalid sum — casting votes that don't add up to exactly one choice (e.g. a "1" for both candidates), effectively voting more than once.
2. Invalid value — submitting a non-binary value such as +2 or −1 where only 0 or 1 is allowed, to over- or under-weight a choice.
3. Copy-paste attack — copying another voter's encrypted ballot and submitting it as your own without knowing what it contains, undermining the principle of a free, informed vote.

The puzzle: how do you prove each vote is legitimate and counted without revealing who voted for whom? That's where zero-knowledge proofs come in.