Paper can be thrown away.. Hidden.. burned.. counted wrong.. etc.. Not everybody can verify the paper. No matter what, with paper, you are trusting it in the hands of a few. You cannot cheat the blockchain. Further, you can make a paper printout with the blockchain that has a web address where any average Joe can in fact verify that he voted for Turd Sandwich.. with a date and everything.
https://blockchain.info/tx-ind... Here is an example of one of my Bitcoin wallet transactions. Notes can be entered for each Wallet location that show what candidate they are (or business.. or whatever). For the life of Bitcoin, that transaction cannot be changed or recorded differently.
For the average Joe to verify, it's as simple as him going to a website he feels he can trust, clicking the 'verify my vote' button.. and typing in his unique voting hash from his printout. The average Joe does not need the same experience it takes to program fucking Bitcoin just as the average Joe right now does not need the experience of counting the whole US set of votes to feel good about his paper ballot.
Like I said, there's probably 1000 different ways voting can be done using the blockchain.. while still making it simple for the average Joe.
Variables don't; constants aren't.