Earlier quoted context omitted.
(without making any claim about "block chains for voting are good/bad") Not really. Generally if you want to privately check something like this, you encrypt it for the recipient (government), and sign it with something that only you know. So the contents are hidden from everyone and nobody knows anyone's signature, but you can prove that your item is in the list, unmodified, and is therefore counted. And then the ch…
Assuming uncontrolled public access to the blockchain, couldn't this also be used to prove to others that you voted "correctly", facilitating vote buying schemes?
E.g. have your signature data be a class of values based on vote possibilities, but have all produce the same final signature. You could produce anything for anyone that way. I'm not sure if that'd be "forward secrecy" or "deniable encryption" or what, but there are a variety of systems that do similar things.
I am not a cryptographer and I don't know any concrete implementations that would have all the properties I want, but pieces of pretty much all things you could reasonably want in a voting system do already exist. And pretty often they can be layered together. The bigger problems in practice seem to be "people won't trust it" (which is defensible), "some of the fancier crypto is too new and not thoroughly proven" (which is very true, e.g. zero-knowledge proofs), and "implementers so far have been stunningly incompetent" (undeniable).
(edit: or I guess more easily, just sign the data after encryption, and throw away your encryption key. then you can claim whatever you like - it's encrypted, they can't know, and you can still show that it wasn't changed)