Earlier quoted context omitted.
There are ways of doing this using encryption so that the person will know what their own vote is in a way that others don't.
"Prove that you voted for Putin or you are out of a job".
About the best I can come up with is a QR code displayed on the screen and on a printout that you can compare with a third party phone app. Machine results are tabulated, and the QR code sheet is put in a lock box separately. This at least provides some way to compare what the computer says you voted versus the QR backup ballot for audits. I'm sure there are holes in my idea.