Paper ballots are really the best solution we have at present and I'd argue the involvement of as many people as possible in counting and supervision is a good thing. With clear evidence like this video of probable fraud and at the very least incompetetence the current touch screen voting machines should be removed at least until they are properly vetted and verified.
Very rarely is there disagreement about what is a valid vote - but they can be very ambiguous. The paper is only approved if there is a high level of unambiguity about it - any doubt it goes out.
I was under the impression that (in the UK) all ballot papers containing anything other than "X" in one box were always rejected for that reason.
Then, in the presence of all the other candidates and agents, I would have go through my list and check off my secret codes.
Guess what? It would kick off big style and suddenly consent to include my magic ballots would be withdrawn by everybody else - the Returning Officer would make a decision and probably have a word with the polis - who are present at, and supervise the ballot boxes.
Protecting the integrity of the ballot is like securing a computer system. Identify the core vectors of attack and lock them down. So it is about "what is the rate of postal votes?" "are the postal vote samples inline with the end-result?" "what is the turnout? relative to last time and other similar constituencies?" "what is the churn in voter registration?" "is the final turnout consistent with the reported turnout?" "is it easy to buy votes?" "is it easy to register fake voters?".
The core point is not to make fraud hard but to make it visible. Of course the basic 'don't make it easy' steps need to be taken - but after that it is all about 'don't let anybody get away with it'.
The problem on HN is that nobody coming up with suggestions on how to improve the ballot is doing any 'customer discovery' - going out to talk to actual people who stand for election and run elections and who are trying to ensure that the vote is fair. The computer pixie dust being scattered around is fixing non-problems.
BTW it isn't an X it is a St Andrew's cross - St Andrew being the patron saint of truth telling - it means 'I swear by St Andrew that this is my true intent'. The 'kiss' on a letter likewise meaning 'I swear by St Andrew that my love is true'. One of the perks of being Scottish is that our flag stands for truth, love and democracy :)
I'm not trying to play Loki's Wager -- there really have been incredibly close elections where you have puzzle out just what the voter intended and it's just not clear. Nor can you make the boundary be "well if it's not clear throw it away," because you can't tell when it doesn't become clear. This isn't the most worst thing ever, but it's part of a legitimate design to want to limit this.
Computer-voting systems do have problems, but they don't have that one. And it at least gives the voter a chance to fix it if they are paying attention.
(Yes, I'm a fan of paper, but it's not strictly better than computer voting.)
Your picture of a someone inspecting a punch-card is not relevant to most paper voting systems - punch cards are like touch screen machines, they are unreliable technology, and should not have been introduced when the previous system worked perfectly well but just required manpower for counting (which can be mostly volunteers). Even the counting could be automated on paper ballots, but you need humans involved for the ambiguous cases, and I'm not sure automated counting is necessary if you have enough volunteers.
Simple paper ballots with a mark inside a square or circle are a tested solution which works well, and leaves an indisputable paper trail in case of recounts. Anything else we've tried just doesn't work as well, though no doubt it has made some companies fabulously rich in suppling the necessary machinery and constantly updating it when it proves to be unreliable.
So I'd contend that paper ballots, as used in the UK for example, are better than the computer voting machines available at present. I'm sure one day we'll come up with better machines, but they'd have to be open source, secure, verifiable and incredibly reliable - the antithesis of the machine in the video.
Count it before the voter leaves, reject any ambiguous ballots with feedback about what's wrong and have the voter fix it before they leave. Repeat until it's accepted.
This is the way it worked when I lived in Indiana. We had paper/optical ballots that were scanned immediately after we turned them in. We watched them get scanned, and could verify that the counter on the scanner incremented (not vote tallies, just a +1 for total ballots cast).
The suggestion is that, when the machine is scanning the ballot, if it finds something ambiguous it immediately rejects the ballot, returns it, and doesn't count anything, the voter gets it back, fixes the issue (or returns the ballot as spoiled and gets a fresh one they can mark correctly), and you repeat.
Nowhere in that does anyone else see the person's votes (except potentially on returning a spoiled ballot, but that's no more true under this system than the existing one if someone notices they mis-marked something, and they can always just mark more to obscure their original intent before handing it back).
The downside of all this is that the machine is still free to slant results if its software has been tampered with.
How close elections are is orthogonal to this issue.