There are mechanisms by which one could both keep the ballot secret and allow a public tally. But to avoid hacking, like the floating-point vote-value in GEMS outlined in another story, the system does require bullet-proof crypto.
Regardless of how the ballots are counted, I do believe there should always be paper backups, scanned, and filed so that citizens can examine them digitally and in person if necessary. With that system one could spot-check any suspected irregularity. Only with such physical redundancy would I trust digital voting systems at this point.
Sometimes there's no substitute for good old dead trees.
https://en.wikipedia.org/wiki/Secret_ballot
Article 21.3 of the Universal Declaration of Human Rights states, "The will of the people...shall be expressed in periodic and genuine elections which...shall be held by secret vote or by equivalent free voting procedures."[19]
Article 23 of the American Convention on Human Rights (the Pact of San Jose, Costa Rica) grants to every citizen of member states of the Organization of American States the right and opportunity "to vote and to be elected in genuine periodic elections, which shall be by universal and equal suffrange and by secret ballot that guarantees the free expression of the will of the voters".[20]
Paragraph 7.4 of the Document of the Copenhagen Meeting of the Conference on the Human Dimension of the CSCE, obligates the member states of the Organization for Security and Cooperation in Europe to "ensure that votes are cast by secret ballot or by equivalent free voting procedure, and that they are counted and reported honestly with the official results made public."[21]
Article 5 of the Convention on the Standards of Democratic Elections, Electoral Rights and Freedoms in the Member States of the Commonwealth of Independent States obligates electoral bodies not to perform "any action violating the principle of voter's secret will expression."[22]
And if I'm understanding correctly (and I might not be), you can confirm that the printout is accurate.
Edit to add: If you can confirm that all of the ids are unique and that the total number of ids are correct, that would go a long way towards verification, along with checking arbitrary receipts against the results, regardless if the ids are pre-printed or printed afterward.
I'd prefer not having any printers involved though. Pre-printed ballots would work just fine and there's one less piece of equipment involved during the actual vote.
BTW, thanks for engaging in this discussion. It's important and it's helping me rethink through all of this.
Another option is making a fake ballot. The local newspaper used to helpfully publish their suggestion of how a devout left wing progressive would fill out their ballot. They're currently the establishment, so they're likely to be the largest problem, and its solved right there.
[0]: https://en.wikipedia.org/wiki/ThreeBallot