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I think you misunderstand. You have a machine that scans ballots, counts votes, and then stores the ballots for later hand-verification. The ballots are fed into this machine in front of the voter. That's how it's done presently in many places (including the polling place I visited today).

The suggestion is that, when the machine is scanning the ballot, if it finds something ambiguous it immediately rejects the ballot, returns it, and doesn't count anything, the voter gets it back, fixes the issue (or returns the ballot as spoiled and gets a fresh one they can mark correctly), and you repeat.

Nowhere in that does anyone else see the person's votes (except potentially on returning a spoiled ballot, but that's no more true under this system than the existing one if someone notices they mis-marked something, and they can always just mark more to obscure their original intent before handing it back).

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