The contradiction at the heart of the problem with cryptographically verifiable elections is that, if you make it possible for a voter to prove to others how they voted, you make it possible for their vote to be bought or coerced.

There are zero-knowledge cryptographic constructions that may theoretically allow you to prove things to a voter without allowing them to prove it to others. But doing this in practice with voters who aren’t cryptographers, and whose personal devices get hacked and stolen, has proved to be a difficult problem.