I would hope, that if it were allowed to be deployed correctly, in a decentralized manner, where consensus was required through different witnesses spread out across the country, that it would be the best thing possible for referendums, candidate elections, even signature gathering to put bills on the ballot.
The technology is there. It just has to be used.
Governments might actually be held accountable for what they do, if their actions required becoming a transaction on the blockchain. It would be there for all to see. I think candidates would have a harder time denying or changing what they say, because it could be recorded in its entirety. I think we could reduce if not eliminate voter fraud through the blockchain, as long as only one account could be created per individual. Keys or passwords would then be enough for identification.
The problem is, obviously, human nature. If people want to game the system, commit fraud, illegally change the outcomes, or unduly influence them, they will seek out and find the way. Will technology be able to stop all that? Probably not from the get go. It will probably take time to get the technology to where it needs to be. It would just be simpler if people would play by the same rules as everyone else, and not come up with way around them.
Of course, if that were to ever happen, we probably wouldn't need a blockchain as much as we do now.