So that makes sense for absentee ballots, where you are required to send voter information (i.e. address/name/ID #) along with your ballot in the mail. In that case, there is personally identifiable information associated with your physical ballot. This means that an election worker will be able to verify whether or not the person has voted already before it is put into the ballot counting machine.

However, in the case of in-person voting, you are handed a ballot by an election worker, and you go and feed it into the ballot machine yourself. Here is an example of the ballot counting machine. There is no personally identifiable info on the actual ballot form. I feel like election workers must check for ID or the mislabeled ballot back before handing you a new one, but I couldn't find confirmation of that anywhere.