[Ajedi32]

One other requirement too.

3) Users should not be able to prove to another person who they voted for

This is to prevent people from using threats of violence or promise of reward to coerce others into voting a certain way.

Unfortunately, this requirement is very hard to fulfil while also fulfilling requirement 1.

[deathanatos]

4. Check that all votes in the tally belong to actual, eligible voters.

Verifying your vote is in the sum, and tallied, is not good enough if the result is swamped with, or more craftily, the balance just tipped by fake votes.

I have no idea how you would implement that.