Earlier quoted context omitted.
Is there any solution where I can verify my vote, but someone can't coerce me into showing them?
There are electronic means if you're a crypto-nerd, but for the general public, paper ballots suit. You know your vote is marked to your preference when you put it in the box, and no-one can make you prove it one way or the other. You should also be able to stick around (or get someone to stick around for you) and confirm that the box you used is included in the counting, should you desire to.
A person goes to the voting center and gets a ballot That person goes to the booth and marks the ballot That person skips entering their ballot and goes out Shows the ballot to the coercer, verifying the vote The coercer gives the ballot to the next person The next person gets another ballot and has the previous one hidden. That person introduces the new ballot, hides the old one and goes out. And the chain goes on.
Apparently it's a common way to coerce votes in low income urban areas and rural areas. You only need distraction or complicity from a person from the voting table and it's hard to detect.
Another common issue is vote stuffing.
On the philosophical part, it is in the end a human problem, but with technology at least you should reduce the possibility of cheating