Public - i.e. everyone knows how others have voted - voting can be both precise and secure. Public voting can be done electronically, say, via encrypted SMS.
Do you know how people take photos of themselves voting at "secret-keeping" poll-stations? How about politicians, which publicly give lucrative promises to their particular electorate?
If they want to sell their vote - it is their choice. I'd only say that the right of citizens to secede from such a society must be respected too.
>Do you know how people take photos of themselves voting at "secret-keeping" poll-stations?
That's illegal, and (somewhat contradictorily) not non-repudiable. You can take a picture of yourself with "ballot marked for candidate I'm paid/coerced to vote for" and then step right out and say "oops, I messed up my ballot, give me another one" and then submit that.
Didn't SCOTUS recently uphold peoples right to take selfies in the ballot box? Seems that ship has already sailed in the US.
Also, California allows for absentee voting with no particular reason. I've voted in every election I've ever been eligible to vote in and I have never once set foot in a physical polling place.