Proving that you voted is different than proving you voted for a specific candidate.
In fact, the one isn't nearly as big of a privacy concern (if any at all). I wouldn't be surprised if someone told me the former could be done with some XOR scheme, but proving that both you voted and your vote counted for a specific candidate while keeping that a secret is a much more difficult task
In Australia, which has mandatory voting, they literally just check your name off the voter roll when you arrive at the polling station. Each polling station has a list (digital or paper) of people registered to vote in that electorate.
After your name is checked off, you then proceed to a booth where you mark a piece of paper before folding and placing that paper into a plastic collection box on the way out.
It's very analog and the electoral commission have no way to know if you actually voted or who you voted for. They only know that you turned up to the polling station and gave them your name.
I assume the number of people who turn up at the polling station, only to walk away without voting is so small that it's not seen as a problem to solve.
Years ago in Argentina, a corrupt politician forced a small community to vote for them using a clever trick. They instructed the voters to fold their ballots into a specific shape or figure. Since the paper wasn't torn or damaged, the votes remained legally valid. This allowed the politician to ensure the exact number of promised votes were in the ballot box during the count
But votes aren't counted by how the paper is folded. Any one of the voters could stamp/mark another name (or no name at all) and still fold the paper as instructed. So, how does that work?
I thought there were ZKP constructions that produce forward-secret receipts, while allowing to re-vote so that only the last vote would count, without ever breaking the original receipt.
In fact, the one isn't nearly as big of a privacy concern (if any at all). I wouldn't be surprised if someone told me the former could be done with some XOR scheme, but proving that both you voted and your vote counted for a specific candidate while keeping that a secret is a much more difficult task