Spend any amount of time around Bitcoin beginners and the one of the recurring themes will be lost private keys.
And "lost" includes countless thefts through network-based attacks aided and abetted by people conditioned for years to take computer security lightly.
If voting identities are controlled by private keys, then voters will lose their voting rights left and right.
Worse, just because an election is "on a block chain" doesn't mean that voter fraud isn't being committed. For example, buying and selling cryptographic voter identities could become a very lucrative industry.