The entire point of a recount is that when the votes are close enough to swing the balance of an election, they're recounted, potentially repeatedly until we can be sure they're correct. They're essentially never more than a few votes off either way. If it's not close enough to swing the balance of the election, it doesn't really matter that a dozen votes were miscounted - we'd prefer that not to be the case, obviously, but not by breaking the other properties of the system.

Short of some very very clever cryptography, you really, really don't want to be able to verify your individual vote, because that means you can verify it to others - the entire point of this process is to avoid coercion, or else there's much simpler solutions. (Pull everyone into the polling station at once and have a show of hands, for example.) You want to verify that one ballot was given to each person registered to vote, and that all votes were counted correctly, but you don't want to verify that an individual person's vote was counted correctly.

If you're concerned with inaccurate recounts, you should be more concerned with systems for which recounts are not possible at all. Like the US'es closed-source black-box voting computers that are currently in use.

Putting aside theoretic possibilities, at this point in time approximately nobody is going to trust a blockchain system. Between "Isn't that the stuff you use to by drugs online?" ignorance and the all-too-real history of everything that has happened with Ethereum to date, that just won't fly.

A ballot design that is prone to getting different results when recounted (hanging chads, etc) is a bad ballot design. Fix your ballot design first.

>Each user gets a new address, and that address is printed on a receipt after you vote. This way you can verify your vote at anytime, and the votes can be counted in public.

Voting receipts like this are bad. They enable people in power (bosses, spouses, etc) to intimidate you into voting the way they want to see and threatening to punish you if you don't because they can force you to prove the way you voted. It also allows vote buying.

Good question. Volunteer to help with your local elections. Learn how it's done.

As for blockchains: Voters sign in before they cast their ballot. If the order in the pollbook matches the order the ballots are recorded, no more secret ballot.

Any crypto- blocko- based system that both protects the secret ballot and ensures the public vote count (aka Australian Ballot) has to create a digital equivalent to the physical secure one-way hash (shuffle) of dropping a ballot into a box.