That's the key right there. When you go to the store to make a purchase, what do you get? A paper receipt that tells you what you purchased, how much money you spent, and the amount of sales tax you paid. In other words, a record of your purchase.
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serial numbers ≠ anonymous voting
ok, but only you would have the 'receipt', so not sure how anyone observing the voter rolls would match that number to yours, and therefore expose the anonymity. A numbered receipt would simply allow a voter to check owntheir vote, to see that it has not changed.
.... and the machine that generates the number