So would it be impossible to make a system that would allow a person to lie if needed and also prove that their vote was wrongly assigned if needed? I've seen

So would it be impossible to make a system that would allow a person to lie if needed and also prove that their vote was wrongly assigned if needed? I've seen cryptographic solutions to things that seem as impossible initially (like having a system verify you know your password without ever telling the system your password and without the system ever knowing what your password is), so I wouldn't be so quick to write off a potential solution to this problem.