>"There are many voting schemes that offer all the benefits of paper voting [...]"

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?