The "system" in blockchain is always a single database file (that changes over time) but that can be downloaded by anyone at any time, and it's history can be analyzed in private and in secret by anyone any time. It has a checksum at any point in time, so you can know for sure your copy has not been tampered with, or even write a web app to allow others to analyze it, and none of the analysis forces anyone to do anything. You are apparently very confused about how this technology works.
I'm very familiar with how blockchains work. But if you can verify your vote then I can tell you to prove to me you voted for the person I told you to.
Someone can also compel me to use my own password to log into my bank account and transfer all my money to them. Every new technology that has ever been invented has always had people like you who can think up highly statistically insignificant scenarios where the technology can be misused.
You think people being compelled to vote for a specific person is an unlikely event? Unions, employers, organised crime, parents, etc have all over the years tried to force people to vote a specific way. If voting is verifiable they can be successful.
Even with blockchain it would still be "secret ballot". Each person would have their own encryption key they use to lookup their own vote. No one could check how I voted unless I allow them to, just like no one can get into my bank account unless I allow them to.
If society decides the risk of these types of behaviors is significant they could pass a law making it illegal to ask someone how they voted. For those who would violate such a law even if it existed, they are by definition criminals, and already have the ability to tell you "Give me your banking passwords, or else". Blockchain itself won't cure all the problems with humans being criminals in this world, but blockchain itself DOES cure the problem of hacker-proofing voting data.
BTW: even if the blockchain data were totally held all within local governments only, it STILL addresses at least the problem of tampering at any level other than where the information is first collected. Even if the blockchain DB doesn't go as fine-grained as per individual it still "hardens the system" considerably from hackers, in a way that paper could never do, because recounts of paper is susceptible to human miscounts (both intentional and unintentional), and blockchain is absolutely not.
Voting is the way it is specifically to combat this problem. Your solution tries to fight against a problem that is basically impossible without systematic widespread corruption by opening it up to localized corruption which is historically common. You're solution doesn't make the situation better it makes it worse.
Anyhow if you can't understand why secret ballots exist after all that explanation I'm never going to be able to explain it in a way you understand so I think we're done here.
Our current voting system IS secret ballot, and IS also ALREADY based on computer DATABASES (not paper). You fail to realize that blockchain is basically just an encryption strategy for databases. It IMPROVES database security. It has absolutely nothing to do with whether votes are kept secret or not. It ONLY has to do with whether it's technically possible to tamper with the data or not.
Bottom line is: paper ballots CAN be tampered with (whether secret or public) but blockchain cannot. Got it now?
