Yes, and there is an easy way of doing that. You give people an ID based on their birth certificate and hash that information. You now have an anonymous identifier which you can tie to a vote. This vote can go on a public blockchain. Any party interested can subscribe to the blockchain and verify their own vote from home while their avatars give a plausible deniability.
People that say their votes were tampered with go back to vote again, which submits a cancel vote and a new vote.