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Using a system like ZCash the government could have citizens register a public address, then 1 token is distributed to each public address, votes work by sending the token to the candidate you vote for, whomever has the highest balance at the end of the election is the electee (this even allows for off ballot candidates, but up to rules). ZCash is designed so that you can't tell the contents of a transaction despite it being immutably on the blockchain

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Another important property of voting systems is that you can't prove who you voted for, so that you can't be forced or paid to vote for someone. A blockchain based solution, even like ZCash does not fulfil this.

You can prove who you voted for by taking a picture of your ballot when you vote. Some thug could rough you up if you can't provide a selfie of your ballot being marked for some candidate

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