The normal person has no knowledge of stats. I am a professional physicist, and I struggle with stats. The methods you suggest can convince a stats professional that the tally is correct. It cannot convince a normal person of the same.
Election security should not hinge on a "trust me bro" - especially when people are being convinced the other way by Russian propaganda talking heads on social media.
Manual counting requires zero trust. In my country anyone is welcome to observe the entire process from start to finish, if they wish to do so. A few years back a fringe far-right party tried importing the voting integrity distrust over here, and recruited people to watch their local polling stations to "expose the fraud". Which was totally fine because they were always allowed to do so, and it fizzled out because zero evidence of fraud was found, and that party still didn't get a significant number of votes.
Don't these two situations (watching vote counts; understanding a complicated statistical argument that the vote is tamper-free) require the same kind of trust?
1. In both cases, everyone is theoretically capable of checking it themselves; they're theoretically zero-trust. In the former scenario, I'm theoretically capable of attending the vote count, and in the latter scenario, I'm theoretically capable of learning the statistics needed to verify the argument.
2. In both cases, most people cannot (or will not) practically check it themselves, and is trusting that someone they trust is doing the checking for them.
I'm not saying they're the exact same situation, but they both ask for a large amount of trust from most of the voters.
You are correct on both points, which you elucidated well. Let's me differentiate the two systems based on "who-to-trust".
- The observe-system operates on an adversarial basis. The people observing the voting process are state officer, independent observer, each party's observers. If you vote for party X, then you trust that party and its people to do right by you. This include trust party X's observer, who additionally is often a local well-known person. You can actively distrust all the other observers and officers, and as long as your observer gives the A-Okay, you are happy with the result. This trust in your observer is a very simple human kind of trust. No expertise is needed by your observer. If you trust other observers, your trust in the result goes even higher.
- The stats-system is founding its trust in the trustworthiness of the stats experts. The problem is that (1) you don't know the stats expert personally. In fact, a huge chunk of the population in any country doesn't know anyone who is good enough at maths and stats. If people in your family are not the math type, your friends will also not be the math type. (2) It is incredibly easy to sling mud at the expertise and trustworthiness of an expert. This process is operating at a very high level these days on social media. Anyone remotely connected to politics is continuously character assassinated by others. Adopting a stats-system actually will actually increase this mud slinging to new heights.
The observe-system is better because as someone else has said, all the counters and anti-counters to it have been known for 100s of years. Breaking it requires breking 100s or 1000s of polling stations across the country. The stats-system has more central points of trust which can be broken more easily.
