So that people can't bribe or blackmail you into voting a particular way.
The ones I know are well armed, but about as non-violent as you can be and not be a Quaker.
The point is: Neither has he encountered union thugs beating somebody up because he was against unionization. It's a ridiculous myth.
But I don't know about 'union thug' being a myth: lots of actual violence back in the dark days of the last century. Carnegie brought in an army to bust up the union and it wasn't because they were meek lambs.
No, it was irony.
I know it's not foolproof as you could request a new ballot, but I'm guessing those buying votes aren't the smartest folk. Plus you'd be crazy to not accept the money upfront, as there's no way they're actually going to pay out after the fact and it's not like you can take someone to court for not upholding their end of an illegal bargain.
For example, voting machines could drop duplicate receipts into a bucket that voters are free to rummage around in.