>"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?

The ballot is secret – as long as the vote counters are not colluding, nobody can observe the votes in transit, and nobody can access all votes. It seems better than most proposals I have seen but I certainly would claim that this system offers "all the benefits of paper voting". And I haven't even mentioned that voters can generate polynomials that gives them multiple votes without anyone noticing.

Like I said, it's a proof of concept that shows it is possible to have transparent auditability and secret ballots at the same time. It's not ready for implementation as it is, though, for the reasons you mentioned.