Did you ever see how the votes from those old machines were tabulated and reported?
Yes, I actually worked the polls several years in a city/district I lived in at the time and the machines were infallible. The totals were visible through openings in the machines. The totals could not be individually changed unless you wanted to break the machine down, remove and reinstall certain wheels, and reassemble - probably easier to take apart a Lamborghini engine assuming you could find someone who could disassemble a 200lb piece of machinery and then get it all back together again without attracting notice. You would also have to do this to many machines to have an impact on the vote. Other than a complicated disassembly of the machine, the only way the individual wheels could be changed was through voting, otherwise a total reset was the only way to move the wheels and this required two or more keys. The machine kept track of total voters and individual votes. Both (or more) parties had representatives who would view the machine totals.
Better yet, we knew the results of the very large district in only a couple of minutes and reported them to the parties and the city. In our fairly large district, we had 10 machines. Adding up the votes for the major candidates like for our mayor or for a presidential election took mere minutes, individual candidates took a bit longer, but in any case, we got full totals tallied in half hour or less.
There was no counting of individual paper ballots, no miscounting, and most importantly, no sudden bushel of ballots showing up uncounted, etc.
Recounting was done by the parties simply going behind the machine and reading the wheels.
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