That's just a record though. A bitcoin style blockchain would provide a hashing-power based method of deciding which votes count in the case of double voting, which isn't required or even wanted in this case.
It's not just a record. It is public and untamperable, and could form the core of vote verification.
I didn't imagine voting to be like spending a bitcoin. Although that could work too. Issue every voter a single indivisible votecoin. To vote for a candidate send the votecoin to their address.
But, perhaps the V initiative have something else in mind for the blockchain. I'm sure there are others.
I've outlined only two possibilities for using a blockchain here, but I'm sure there will be others.
You haven't given a reason to use a blockchain, you're just pointing out ways in which you could use a block chain.
As I said, why would you rely on a democracy of hashing power for anything when you have unique underlying identities you're trying to let vote? Why use a system designed to allow the decentralized use of a currency without double spending when double spending isn't an issue?
The two biggest issues solved by Bitcoin are double spending and distribution of a decentralized currency. Our would-be voting system doesn't need either of these things.