In Minnesota, honest counting is enforced by process. Any ballot handling, whether marked or unmarked, requires the presence of members of at least two different parties. At no point is a single person (or group from just one party) ever left alone with ballots.

We've had two full-on hand recounts at the state level in the past decade or so, and the final results where within a few hundred from the original count in each case, with three million votes cast. Good process solves a lot of problems.