There would be no way to hack the vote if it were done on the blockchain. The only way that it could be hacked is with a 51% attack, but it would be hard to accomplish if, later discussed, wallets (a Voter ID with a chip) were destroyed on death or invalidated (where necessary) if they become a felon and unable to cast a vote in certain elections.
A wallet, and your passphrase, would be essentially private. The only way you could cast a vote would be with your "wallet" (or chipped card/Common Access Card), and you could only ever change (if done on time) or cast a vote with the physical card. Issuing cards could improve voter turnout because you could cast your vote from home at any time, not relying on polling station hours, if you also bought a $10
Common Access Card reader, or cast it from a friend's or neighbor's house who had one. Though, polling stations would still be operable, but you would have bring your Voter ID to cast a vote.
There would have to be a system in place so that two or more Voter ID cards couldn't be issued to the same person, a system that destroyed the wallet on death (or invalidated it if they become a felon and unable to vote), and a system that would reject a Voter ID card if it was reported as lost or stolen, with obviously a new one issued to vote again.
I don't know enough about the blockchain to where you could privatize your vote, as nobody should be able to see that, or even if you voted at all. That information should only be visible to you through the voting portal and who you voted for if ever accessed. The only information that should be public is the number of "wallets" that placed a vote for which candidate to tally the votes within seconds to determine the winner on the spot/after polls close.