This is why I I decided against saying "impossible" and instead "hard if not impossible". :)
I'm not 100% certain it is impossible, as there are certainly some clever possibilities that become available with zero knowledge proofs. The big issue I see is that it has to somewhat go beyond ZK proofs, as you can't have a situation whereby the voter can in a separate channel show how their vote was cast.
For example, Charlie votes for Bob in a ZK way, so Alice does not specifically know /how/ Bob was elected, only that the result of the election is true. This is a great start, but the issue is whether or not Charlie can tell Bob (off-chain) "hey, I voted for you, here's my side of the proof." Bob could then incentivize Charlie after the fact, without Alice being aware, and the issue remains.
Ah, good point. So I guess you need a zero knowledge proof where it's not possible to prove that you submitted the proof! Now my head hurts :-P
On a somewhat unrelated note, I just went to a talk by Lane Rettig who was until recently an Ethereum core developer and left to work on a new project called SpaceMesh which has a pretty cool new consensus algorithm designed to address a number of the issues with traditional PoW. Just thought you might be interested.
Yes, it's quite the puzzle!
Sounds cool, I'll check it out.
How practical would that be to arrange on a large scale?