Only if the crypto is designed to be run in your head, so that you can lie to someone who wants proof. Good luck implementing that through education. Consider

Only if the crypto is designed to be run in your head, so that you can lie to someone who wants proof. Good luck implementing that through education. Consider the simplest case, a binary choice. The system tells you (and only you, and only once and without tangible record) that the public copy will either be inverted or not, a one bit one time pad. Kind of feasible, but already hard enough: will you really assume tampering when the bit that makes the public record match your vote does not match your memory? Then imagine scaling to something more meaningful than a binary vote, even just to more than one binary. I can't see that actually working out.