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.