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>What if every vote had an ID / random number attached to it, identifying you

Votes must not be attributable to any given person, or else the potential for coercion exists.

I read GP as simply verifying that a particular ballot made it into the count, not verifying what the votes on that ballot happened to be. That seems less problematic with respect to buying or coercing votes. I'm not convinced that "lost ballots" are a big problem, but such a system would be a way of checking that.

Or vote buying.

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