What we need is a zero-knowledge proof: we need the entire voting dataset to be publicly downloadable and some kind of checksumming so that, while maintaining anonimity, I can 1)check that my vote is the same 2)run whole the counting in a blink on my PC.
This gives much better guarantees of no tampering
3) Users should not be able to prove to another person who they voted for
This is to prevent people from using threats of violence or promise of reward to coerce others into voting a certain way.
Unfortunately, this requirement is very hard to fulfil while also fulfilling requirement 1.
Verifying your vote is in the sum, and tallied, is not good enough if the result is swamped with, or more craftily, the balance just tipped by fake votes.
I have no idea how you would implement that.
I suppose the only benefit of people is that they are more difficult to coordinate.
In a properly run paper election, there is no individual that you have to trust. In principle, anyone can go and watch, and usually there are representatives of many/all parties in every polling place, watching every step of the process. It's not just that people are more difficult to coordinate or control in general, it's that if someone distrusts you, they can come and watch for themselves.