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We have the solution it's just not practicable. Cryptocurrencies and hardware wallets have solved this problem. But they operate at the scale of people in their bedrooms not hundreds of millions of people voting over one day all over a country.

Passports would need to become like hardware wallets with screens such as Trezor. Who's firmware and design are open source.

The screen means I can see what I'm signing and later be shown what I signed.

Now, I don't want people to know who I vote for. So we make it e-passport gate so that no one can enter with me.

Now I want to be able to verify my vote at a later date but not let others know it was me. Well this too is solved by multiple cryptocurrencies like monero and z-cash.

I can go to my local town hall enter a room alone using a e-passport style gate and check my vote at the machine. My device can verify my vote.

Someone with the vote can only see that 1 of N voters did it. Where N is so large they can't identify me.

No duplicate vote is possible.

Literally no one would agree to this however.

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As long as you can see your own vote, someone can force/coerce you to show them your vote.
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Not necessarly. For example you could have the machine print a ticket with the vote and show it to the voter behind a window. The voter:

- confirms (paper goes down the box) and exits the booth

or

- cancels (paper is burned) and votes again

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Cryptocurrencies mostly are pseudonymous, and, really, not even that. Certainly bitcoin is at best pseudonymous.
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There is a reason monero and z-cash are being banned in Europe.

I can't claim to be a crypto expert.

But hiding a transaction and it's value among other transactions is perfect for voting.

As I understand it Monero uses ring signatures to make it so it's not possible to know which individual of a group initiated a transaction, and it's zero knowledge proof system means it can be verified that a particular transaction is valid despite this.

To my layman mind that seems to be good enough, every vote can be verified by any party as valid (no double spending or double voting took place).

You can never narrow down who made a particular vote beyond a large pool of people.

You can't tell where any transaction went (you don't know who was voted for).

At the same time with my private key I can see my vote.

The only thing needed for voting is the e-passport style gates.

Certainly it won't just get a case of use monero, they would need to design the system for voting.

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True for bitcoin but Monero is legitimately quite anonymous
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You can always include a nonce to decode the votes true value or provide an alternative for people that are vulnerable to coerction. If you need an example: monero crypto currency is the pinnacle of it.
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You could have verification be done in person and not online with no way to share it.
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You'd have to go to your elections authority's location, and very few could do it w/o overwhelming the vote verification rate capacity, and very few would.
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retraction of vote with a new vote solves this.

Since I'm able to retract my vote, I cannot sell it. And since I can retract my vote, I cannot be coerced in any way.

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Elections results have to be final at some point, and after that point no further retraction/changes can be made, therefore you can be coerced.
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coerced at the time of voting, but then you can go back and simply change it again
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And then you can be coerced again, and again, until the vote is final.
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there is a limit of how many people you can be physically present to coerce up to end of election, making it inviable en mass, thus impractical.
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how would one know? they're they know a transaction happened, but they do not see the contents of a transaction
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