I'd recommend the various talks and papers J. Alex Halderman has given/written on this topic, especially on Estonia's e-voting system.
A major benefit of paper voting is that you don't need a math PhD to verify for yourself the integrity of the vote process.
Just an example from another field: It is easy to compare key fingerprints shown by WhatsApp/Signal/GPG but how do I know that the software does not encrypt the text with a second key? Personally I am not competent to do so and have to trust others. Don't forget that it's not enough to audit the code itself but you would also need the check the whole build process from scratch (and processors it was done on for that matter - and while we are at it: how can I know that the display actually shows that it was asked to do?). How many people know how to do so?
When I've thought about e-voting it's seemed tractable except the conflict between verifiability and keeping the ballot secret. I'd be interested to see how such schemes manage this point in particular.
It's a proof of concept, it still has drawbacks, but it proves that you can have a system where all the votes can be accounted for without any information being revealed about any individual's vote: the ballot is secret.
You appear to have one incomplete theoretical scheme?
Thanks in any case for sharing it.
Edit: just on a quick reading - if I think I'll lose a seat, and can corrupt a single authority, I can get them to return a random set of numbers for their part of the polynomial, this randomises the results, doesn't it, giving me a chance to win. As there's no verifiability, it can not be observed in the voting data?
Is this legal?
According to German law this is illegal. Thus we're based in New York and the website is served from the US.
But of course, postal votes make vote selling possible.
It is not. There are many voting schemes that offer all the benefits of paper voting together with the verifiability and transparency of cryptographically verifiable vote counting.