I only have a moment as alone with the baby who is a little demanding today but, I would assume that if there was a unique key provided for a voter that was known (connected to the voter. When it is used it can be burned. But, the vote it casts randomizes the information and disconnects it from the voter. That way, it is possible to know if the key voted but, not how it voted.
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I'm not sure I understand how this is supposed to work 100% and I'll consult with google on this topic too, but this sounds like a system that is prone to abuse. If the keys are burned, how do you check that the vote wasn't fraudulent. When issuing keys, you need to check that the voter indeed has a right to vote and hasn't gotten another key already. That's a single point of failure where somebody could issue additional keys and having keys burned (though that's the part I'm not sure I understand) means you wouldn't be able to catch them.
Have a great day with your baby! :)