There are some issues need to be solved:
- System's user can have only one «account» (or «wallet») to vote. Nobody can vote twice.
- Nobody can't see your vote. To be clear, everyone can see it, but didn't know that it is YOU.
As I know, first issue is hard to implement, without making second one... But it is temporary problem =)
Blockchain would allow for votes to be stored in a system, where it would be near impossible to change them. Unfortunately, the problem with a lot of elections is not the transmission or storage of votes. What you would need to do to is control the input. Corrupt governments often falsify elections by forcing people to vote and by voting for people who they know won't vote anyway. Blockchain would not fix this problem. It may help make elections more secure, but there are a lot more problems to deal with.