What about this? Consider a toy system: everyone gets issued a UUID, everyone can see how every UUID voted, but only you know which one is your vote.

This is of course flawed because a person can be coerced to share their ID. In which case you could have a system in which the vote itself is encrypted and the encryption key is private. Any random encryption key works and will yield a valid vote (actual vote = public vote + private key), so under coercion you can always generate a key that will give the output that you want, but only you know the real one.