Payments is definitely something blockchain can do better in some cases
I am in general a blockchain skeptic - I think in most cases, there’s just enough trust to just use a centralized database - but voting seems like a good usecase for blockchain, as it provides voters with a receipt and it’s designed for auditing provenance.
This is, in fact, undesirable. If verifiability is possible by an individual someone can ask you (under thread of violence) to verify that you did or did not vote a certain way. It's especially undesirable if verification can be performed a long time after the vote is completed because laws and social mores can change turning a previously innocent vote into a black mark.
There are probably even better methods to further protect both anonymity and verifiability. I don’t know if the group at (2) is still active, but the graphic presented there looks like a good setup—-though I think they are after vote-from-home, while my linked comment still makes use of polling places.
(1) https://news.ycombinator.com/item?id=14921442
(2) https://followmyvote.com/cryptographically-secure-voting/
There's an enormous difference between trusting the government to _count_ the votes correctly and trusting the government to _record_ the votes correctly, and I think this is actually the point. How do you enable voting _without_ trusting the government?
If you have a public database then you can sign votes into it, but how do you ensure that the government won't simply delete votes it doesn't like? Pretty soon you get to the idea that each vote should be incremental to all the votes before it, so no one can manipulate the previous votes... and you get a blockchain.
A blockchain would allow you to separate the act of voting from the tallying of votes, which would be an enormous improvement over the current 'check everyone's eligibility at the door and don't mention how many people you turned away'.
Of course, in neither data format do you have any way of actually authenticating the other votes, by design. Maybe the vote in the block before yours was a dead person, or never existed at all, how would you know? (this is what the crypto world calls a "sybil attack") Whoops, looks like we're back to trusting a centralized authority (the government, who issues the voter tokens). So why do we need millions of computers hashing away, again?
Fundamentally, one of the design features of voting is that it's un-verifiable, i.e. you can say you're voting Bush and go into the booth and vote Gore, and nobody can prove otherwise. Otherwise you could have personal threats against you (boss/spouse/etc) and if you have a ticket that can be verified to show you voted Gore then you could suffer personal harm. Verifiability to the public is actually an bug in the system here - it should be verifiable to the government and no one else. The best systems produce a paper token that is retained at the voting site. You can then validate the number of tokens against the voting rolls/etc, but the "evidence" stays in the possession of the government (who we've already agreed must be trusted anyway since they're the ones maintaining voter rolls/issuing tokens and ballots/checking IDs/etc).
I forget what the name of the theorem is, that says identifiers like domain names or onion names can either be unique/authentic, intelligible, or decentralized, pick any two. Well, you can also say that ballots can either be publically verifiable, trustless, or private, pick any two (where "guaranteed one-per-person" is a form of trust). Blockchain doesn't escape this, it is just a different format for the data (Merkle tree vs flat CSV).
In many European countries we do have that, as we carry our national ID cards[0] that have their own private key for signing documents and authenticating. Signing a vote securely isn't a problem but then the problem comes on how you sign it and keep it anonymous simultaneously. Also of course we trust that the state doesn't keep the private keys somehow when creating new cards.
[0] https://en.wikipedia.org/wiki/National_identity_cards_in_the...
That's what I mean by the difference between counting votes and recording votes. All the dead people throughout history could record a vote, but that's doesn't mean they all have to count in terms of who gets elected.
All you would need is a private key given to you by the government that is associated with your identity that you use to sign your vote. Then the government can only count the votes by the identities it trusts.
Edit: Example - people vote against unpopular candidate Paul. Paul then stages a coup and takes control of government. He then asks you to provide a receipt that you voted for him on the blockchain or all your property is confiscated by the state.