Earlier quoted context omitted.
It would be pseudo-anonymous like Bitcoin. You would keep the mapping between public keys and real-world identities private. But perhaps some percentage of people would choose to waive their right to privacy, further strengthening trust in the system. Statistically, the public voters should be in line with the final outcome.
> But perhaps some percentage of people would choose to waive their right to privacy, further strengthening trust in the system. This has the same problem. Didn't waive your right to privacy and provably vote for the right candidate - you're fired (or worse). That's why taking photos of a ballot isn't allowed, you can't have any way to show who you voted for.
However, your "or worse" note still applies. E.g. a local gang could do the same thing, and they are unlikely to be stymied by illegality.