[DrPhish]

Scrutineers : https://en.wikipedia.org/wiki/Scrutineer

You have a number of differently affiliated persons watching the proceedings, and having at the end a rough idea of the number of votes that were returned per polling station. Then (with some coordination that should be trivial for the smallest of political parties) those results can be independently reckoned and compared back to the official totals. Any irregularities should be quite obvious. Recounts are probably the Achilles heel of paper ballots, as you need a way to verify that they were not tampered with in the meantime

[vacri]

Scrutineers also have the advantage of being understood by anyone with a pulse. "Votes go in here, mutually opposing interests watch them like a hawk until they get to the counting center, then the count is watched by those mutually opposing interests. You can be a scrutineer yourself if you're concerned. The record can also be re-tallied if there's a concern".

Compare to voting machines: "Just trust us. You need to have deep domain knowledge in several fields before you can even start to evaluate our trustworthiness (software, hardware, security, etc)... so just trust us. No, you can't examine the machines."