> but voting is supposed to be anonymous

It's actually much much worse than that. Votes not only have to be anonymous but not verifiable by the voter (i.e. they should have no way to prove who they voted for after their ballot is submitted). You don't want to live in a world where rioters could target anyone who couldn't prove they voted for their candidate or domestic violence for the same reason. Also, if votes are verifiable then it becomes easy for a person to buy votes or for companies to offer 'incentives' to vote for a particular candidate.