What would you hash, though? The name? The SSN? These are all know plaintexts…

If you want to de-anonymise a vote with any of these you just make a rainbow table of all voters.

Do you add salt? But now salt becomes a secret… how does the secret is picked? Someone centrally? Back to rainbow table. Everyone picks one? Then the voters has to write the hash… at that point there is no benefit with an unique id that is not really anonymous