There might be something usable in a web of trust fashion, that only the original poll author can publish a verified set of votes from people withing their sphere. 

This moves the attack vector to the original author, but maybe there's something possible with verification of all 'approved' votes by the author.

So, if you vote, you have to prove a certain 'closeness' to the vote author, and if the author closes the poll (or publishes intermediate results), a proof of the set of votes needs to be included.

But now I'm going a bit out of my depth.