Technology has bestowed a stunning twist of fate in the arcane world of counting how America votes.

A decade ago, activists railed against private companies who made the computer-driven "black boxes" that tabulated election results. That opacity, to protect their trade secrets, fueled sore losers and conspiracy theories and thwarted journalistic investigations of miscounts or tampering.

But today, the voting machine industry's newest devices are producing digital images of individual paper ballots, accompanied by devices that mark the ballot or its image, and include audit systems that can trace disputed ballots back to their precincts—by using technology that's akin to how banks allow smartphones to securely deposit checks.