Perhaps this could be combined with a zero-knowledge proof? From wikipedia[1] with context:
zero-knowledge protocol is a method by which one party (the voting machine) can prove to another party (the voter) that a given statement is true (their ballot was cast, untampered), without conveying any information apart from the fact that the statement is indeed true. ... the definition implies that the voter will not be able to prove the statement in turn to anyone else (a vote buyer/intimidator), since the voter does not possess the secret information.