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From an efficiency point of view, voting at elections online seems to make a lot of sense except that there is currently no way to have a completely trustable electronic voting system because of the lack of the ability to verify it, e.g. source code, transactions matching input, etc.
Blockchains seem like they could provide this function, but I've probably missed details – what are they?
Remember, this is in the context of national voting system where nations stick to paper based voting because they have no other way to verify and audit the accuracy of the vote.