You could do such a hybrid system, but honestly purely paper based systems seem to work well enough in practice. Eg Germany uses paper and human counting, and the results are usually available fairly quickly.
The problem with randomly hand-counting a few boxes of ballots is that you then need to convince people that the random selection was uniform and fair and actually random.
There are methods to do that, but there are at least as complicated and full of cryptographic finesse, that they ain't simpler than vetting an electronic voting system in the first place.
Having said that: human counting isn't fool proof and is still open to abuse and tampering.
It's mainly that any village idiot can in-theory audit the human-run system, and that it would take a conspiracy with lots of people to engage in wide spread tampering.
The more people involved, the harder it is to prevent leaks.
The problem with randomly hand-counting a few boxes of ballots is that you then need to convince people that the random selection was uniform and fair and actually random.
There are methods to do that, but there are at least as complicated and full of cryptographic finesse, that they ain't simpler than vetting an electronic voting system in the first place.
Having said that: human counting isn't fool proof and is still open to abuse and tampering.
It's mainly that any village idiot can in-theory audit the human-run system, and that it would take a conspiracy with lots of people to engage in wide spread tampering.
The more people involved, the harder it is to prevent leaks.