Read this algorithm: https://en.wikipedia.org/wiki/Homomorphic_secret_sharing#Exa...

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.

>"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.

From what I understand, verifiability and transparency is something you don't really want because it enables vote selling. In a secret ballot, someone dishonest enough to sell you their vote is probably dishonest enough to vote the other way.

You can already sell votes, see this start-up: https://www.votebuddy.de/

Quite telling are their FAQ:

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.

Just FYI, that site doesn't actually do anything. It is designed by the Peng Collective to create outrage, nothing more. The same happened during the 2000 US presidential elections with voteaction.com, a German-based site (as it's against US law) that turned out fake as well.

But of course, postal votes make vote selling possible.