I'm not sure about this specific approach. As other comments note, this is somewhat complex. That said there may be a few gem ideas.

- Did my vote get counted? (can you prove it)

- Did it get counted correctly? (can you prove it)

- Can a vote be both traceable to the voter and anonymous publicly?

The parallel to blockchain is simple. I get a "vote coin" that I can spend at the election. You can then see who has the most votes. The challenge to overcome in any block-chain approach is how to prevent votes from being bought and sold.

If done correctly you don't have to trust the hardware to trust the election. If done correctly we could vote by phone.