A voting system where voters can prove which way they voted is vulnerable to coercion or retribution.

The manager rounds up the workers and "suggests" they all compare how they voted. Those who voted "pro-company" will likely reveal their vote. So for everyone who refuses to reveal their vote, the manager checks a box next to their name on the attendance sheet.

There may be a voting system that provides all the desired guarantees, but I doubt such a system is also easily understood and trusted by the average voter.

You can partially defeat this by allowing people to change votes. Then everyone has something that "proves" they at some point voted pro-company but they could have changed it later.

Ok what about when you're coerced to change your vote?

You change your vote, collect your reward, and change your vote back again?

Just make that kind of thing illegal like so many other things around union elections and come down on them like a ton of bricks if they violate this. Both the employers and unions.

We have secret ballots because this is not a solvable problem. If you're threatened with your job it is one thing, if you are threatened with violence for voting "incorrectly" it is another.

Current protocol: Alice sends her personal information and vote in the mail to Eve. TV tells Alice that the system is secure.