If each ballot is numbered and recorded, then how is the voter’s identity kept secret?
It would be a simple matter to match the number with the voter.
It would be a simple matter to match the number with the voter.
The ballot number is recorded as being used. The voter is recorded as having voted. But the number of the ballot is not recorded with the voter's name.
At the end of the day, the number of ballots cast must equal the number of voters, and all spoiled or unissued ballots must be accounted for.
This prevents a poll worker from just marking up all of the unissued ballots and running them through the machine. They would also have to mark off an equal number of voters as having "voted."
However, Poll watchers are given access to the same voter database that the precinct uses, so they can see who voted and when, so a poll worker can't just magically mark 500 voters have voted after the polls closed.
At the end of the day, all theoretical voters have had their names check marked, but no one knows who got which numbered ballot, unless they separately recorded the name and ballot number of each voter. Then, after the ballots were cast, they would have to be pulled and matched with the unauthorized list.
The votes are tallied and the total shows that a thousand ballot were cast. It doesn't necessarily show who Mrs. Smith voted for, or for that matter who anyone else voted for. And, in each election, there are undervotes. So while a thousand ballots were submitted, there are going to be blank votes for some candidates or propositions.