You could also add a second layer of security here pretty easily. People would probably need to be given a printout with their hash on it. To avoid this receipt

You could also add a second layer of security here pretty easily. People would probably need to be given a printout with their hash on it. To avoid this receipt being proof, that receipt would include a large number of hashes with various voting combinations also shown. The voter knows which hash is his, but nobody else does. And he's free to claim whichever one he likes for himself. To solve the issue of first voters (when there would be no other valid hashes for their printout) simply seed all candidates with a billion votes to start. Which hash is real and which is 'fake' is irrelevant since all that matters is the sum total of which we know 1 billion are to be removed.