If you're trying to buy my vote, and I'm trying to sell it, I could give you my unique anonymous number, and you could verify my votes. But I could also vote a different way, lie, and give you someone else's unique number, and you'd have no way to know.
You could ask for a special ballot too, where, for example, I vote a particular pattern (yes/no/no/yes/yes/no), to encode things, ideally picking ones that aren't likely to come up in practice, or other complex schemes, but these generally have work-arounds.
At the end of the day, though, it'd be cheaper and easier for you to require me to wear a pinhole camera to vote, do a mail-in, or otherwise. Plus, we had open voting for much of history, and it worked okay. If we went back to the risk of illegal vote selling versus the risk of wholesale election fraud, I'd take the former which seems like the lesser of two evils (and much easier to police too).
The question I've had with this is whether you can prove who you voted for. If you can, you can sell your vote and prove tongue buyer that you voted correctly.
That's also my concern with mail in voting.