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> That's only possible if you sacrifice some of the stronger anonymity requirements

Untrue. You can use strong encryption to ensure confidentiality and zero-knowledge proofs to ensure integrity. Then, you can use methods from homomorphic encryption to tally the ballots. There is a whole area of research dedicated to this.

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So in your opinion the problem is (theoretically) solved? As in, we can have anonymous, verifiable, online, direct democracy such that 3rd parties cannot verify your vote without your private key?

As I said in another comment, individual verifiability and non-coercion are mutually exclusive online. However, there are indeed solutions for the other properties (including global integrity), and compromises between individual verifiability and non-coercion. For instance, you can have a look at Helios [1] or Belenios [2]. Current research is looking for stronger guarantees, a better compromise, or a more interesting voting system (such as Single Transferable Vote or Majority Judgment).

[1] https://vote.heliosvoting.org/

[2] http://www.belenios.org/

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