Paper receipts are crucial to voting.
I think we should return back to paper ballots. When there are witnesses to elections, I don't think any of them are qualified to judge if an election has been done in a honest fashion. This would require experts on the voting equipment where they can guarantee that it has not been tampered with and that is too high a burden and something that complex can not be trusted.
One way it's done is that after entering your choices on touchscreen, you see the printed receipt through a glass window, and then it's stored so a recount can be done if necessary.
However, an electrically scanned paper ballot seems a lot simpler.
I actually believe this is actually the best possible situation.
The voting machine should print a clear, unambiguous, ballot and on-screen tell you to verify it before you officially "cast" your vote. "If the ballot below does not represent your choices, please click <HERE> to request an attendant."
I'm thinking of this more as having printers that print out an unambiguous completed ballot and less as voting machines that "also print out a copy".
I don't think you should leave without (at least seeing) proof that your votes were properly and accurately recorded.
If that means that you have to be given a "receipt" with the names of those you voted for on it, well, so be it. It isn't like your name and/or any other personally identifiable information would be on it -- just the minimal details needed to achieve the singlemost important purpose: verification.
Now imagine cults and other groups that pressure their members into producing those receipts with the correct candidate on them... or else.
The proof would be a paper ballot that you turn in. Your actual vote.
A printed receipt, from an electronic polling place could just as easily be placed in a secure box prior to leaving.
It's amusing watching "ballot selfies" issue too -- it seems that folks just don't understand how important it is not allowing any coercive force influencing or verifying your vote.