Once in the voting booth, how do you know the hardware or software haven't been replaced or tampered with? How would election officials know it? Open-source/har

Once in the voting booth, how do you know the hardware or software haven't been replaced or tampered with? How would election officials know it? Open-source/hardware won't help you - it's still fundamentally a black box, and must be provable secure solely based on its inputs and outputs.