[Animats]

The machines San Mateo County uses do that. After you've made all of your selections, your votes are printed on a paper roll which appear behind a window, with a big bar code at the bottom. If you approve, the paper is wound out of view so the next voter can't see it. You can reject the printed version and go back, in which case the paper is marked with CANCELLED or something similar.

At the bottom of each voter's paper roll entry is a big bar code. This allows quick recounts by running the paper roll through a machine that reads the bar codes. A full manual check is also possible, but slow. The system goes through miles of thermal paper for each election, but works OK.