Well, I always feel the urge to redeem myself after proving I am an imbecile. Because of this I involuntarily considered secret balloting in the back of my mind since you corrected me.

What if there's two hashes formed, one which pertains to the vote, confirming a vote based on the asset involved occurred, and one which inures to the asset itself, which the voting mechanism will not allow to vote again?

This is not quite trivial, but I suspect it is doable.