1. A single-pass method of authenticating and sorting mail items of a received batch of mail items, the mail items including return envelopes potentially containing ballots for a vote-by-mail election, the method comprising steps of: in one pass through a sorter system, reading by way of a reader device, each respective mail item in the received batch to acquire data including: (a) mail item verification information; and (b) a representation of a portion of the respective mail item expected to contain a signature of a sender of the respective mail item; in the one pass through the sorter system, for each respective mail item in the received batch: (1) determining whether or not the respective mail item is authentic, by: (i) determining whether or not the mail item verification information satisfies criteria for an authentic mail item; or (ii) determining based on the item verification information whether or not a ballot has previously been received from a respective registered voter; and (2) determining whether or not an authentic signature is present on the respective mail item, by: (i) comparing the representation of the portion of the respective mail item expected to contain the signature to a prestored representation of a signature of the respective sender, the prestored representation being stored in a reader database associated with the reader device, and (ii) determining from the comparison whether or not the representation of the portion of the respective mail item sufficiently matches the prestored representation of the signature of the respective sender; in the one pass through the sorter system, sorting each mail item in the batch determined to be authentic and for which it is determined that an authentic signature is present, into a plurality of sort bins designated for one or more precincts for authenticated mail items; and in the one pass through the sorter system, sorting each mail item in the batch determined to not be authentic, determined to be a duplicate of another mail item, or for which it is determined that an authentic signature is absent, into at least one sort bin designated for mail items that have not been successfully authenticated.