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General Idea: Multiple groups of bipartisan hand counters check each other on their subgroup of ballots. This is highly likely to remove all error in counting, but if there is still error, if the ballots have been randomized to begin with, then each hand counting group will have similar results within statistical tolerances. Finally, if hand counters are insufficient a machine scanner can be used because it too is being checked by simultaneous hand counts, eliminating the risk of substantial scanner error or tabulator hacking. If the final computer used to report results is modified, defective, or hacked, the paper trail of the counting handgroups would reveal it.
Same idea above, just in more detail:
If all the paper ballots are counted at the precinct level (either fully or to the extent time allows), then sent to central counting, shuffled or randomized in one large bunch but just marking each as an absentee, provisional or election day vote for statistical purposes, then the entire randomized group would be homogeneous.
Within the homogeneous group, you then split into various groups for counting, each of which has reps of all parties plus independent observers, and they use the counting method that is most accurate: nobody moves on until we all agree on the count.... this virtually eliminates human error and error generally so long as motivated people at cross purposes are present who are not outright crooks, but the crooks are under intense observation by others.
Separated into separate groups with several to many motivated observers in each, it will be nearly impossible for a group to cheat or make a mistake.
But IF THEY DO, since we've randomized the whole population if there are any statistically significant differences BETWEEN groups, we will know to do a recount right away, or, to be more precise, not to release any initial counting totals until double or triple checked.
The additional advantage of this approach is not just accuracy, but also speed: If the number of ballots are just too high for the number of available human counters, a machine scanner can also be used by humans to speed up PART of the counting, but even the machine scanner is being cross-checked by the groups of human hand counters.
Thus we get initial accuracy, we get all the speed we truly need, and it's done mostly with volunteers (even partisan ones) so it shouldn't be hard to staff. But in the worst case scenario, if we had to hire some of the hand counters to have enough, this is a wonderful jobs program that also teaches people about their democracy and will increase their pride in our societal commitment to accuracy and fairness. That should be a good temporary jobs program, perhaps even high school government classes would get the day after elections off so they can stay up late and know one of the answers to what they can do for the their country....
An additional possible fallback is if there are simply too many races on a ballot every now and then, the elections department releases the full counts on the HOT races (at least those expected to be close before the election) on election night or the morning thereafter, along with the PARTIAL machine scan results where machines are used. Then the hand counts and checking can be finished up later on for all the races, with the cross checks as identified above.
I think this would work, would make sense to the average citizen, and would be something the loser of the election could trust. (the most important standard, since winners always trust the system). It also has the benefit of getting rid of and being more accurate than touch screens.
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