There are many cryptographic solutions to election technology but none of the sane one rely on any form of blockchain.

What we have now is atrocious: black boxes that tally votes like a video game tallies high-scores. We can easily improve upon that, and the fact that we haven't has led some (including myself) to believe that politicians worldwide don't place this issue high on their list of concerns.

What I can envision is a system where you offer credentials, perhaps even biometrics, to place your vote in a supervised facility. Then after the election the government publishes a file on a website which any citizen can use to make sure that (1) the votes were counted correctly, (2) their votes actually appear in the list, (3) their votes were assigned to the candidates they actually voted for. (And added to that, as OP said, other people should not be able to see my votes.)

What I cannot fathom, however, is any form of voting which relies on a Proof-of-Work.