I've also thought about this.

Each voter visits the polling station and is given an address to vote wih. The voter enters the polling booth and applies their vote against their address. That vote goes into the blockchain.

It would be helpful for expat voters too. For example, in the UK, to register to vote as an expat, you have to have a paper application form posted to you that you then send back with your vote. This is impossible for expats without a PO box. An expat could register online and apply their vote. Using the blockchain, the voter could link their passport/national insurance number to their vote so that it's 1:1.

One definite downside would be the end of David Dimbeldey and election all nighters!