Universal verifiability must extend to ballots themselves. Whether electronic or paper, ballots must be made traceable to a polling center through mathematical verification, ensuring a corrupt chain of custody cannot tamper with the paper ballots.
Ballot traceability provides an audit trail: a set of ballots can be proven to be exactly identical to a set cast and collected in a public setting open to all who wish to watch over the election. If a ballot box goes on a truck and comes off with more, fewer, or altered ballots, the proof used to identify the ballot set will not match up.
With simple plurality voting, we can achieve this by disclosing the simple vote count at the polling center. Anything using ranked ballots requires high-complexity mathematics or a full copy of the original ballots.
Large sets of data, such as full copies of hundreds of paper ballots, take a long time to produce and verify, and lead to mistakes or outright manipulation. Generating proof for advanced voting systems requires the use of a computer, and so we focus heavily on methods of verifying electronically-cast ballots without putting the state of the machines at risk.