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there is a big problem with that movie. the scenario is one single county or state with 100 precincts. Any statistician, or decent math student will tell you, that of course if you run the test one time, or two or three times, there is a certain percentage of a chance that you will pick the brown peg. I believe this is the math:
Let's say there are 5 brown pegs and 95 white ones.
If you do a 1% audit (pick one peg) you have a 1 X 5% chance of picking a brown peg.
if you do a 5% audit, you have a greater chance of finding a brown peg, but it is still a relatively small chance, it would be somewhere around 25% (not exactly because when you pull the 2nd peg there are only 99 pegs to choose from, not 100.
The point of the exercise is to say, do you want a 25% chance of catching a stolen election?
That argument is flawed, because in reality there are thousands of towns and counties. the same experiment is essentially repeated over and over again thousands of times.
In that scenario, a brown peg would almost certainly be picked eventually.
in other words. let's say you have 25-sided die, and you color one side of it a different color. If you throw the die one time, you probably won't get the colored side up. But if you throw the die a thousand times, you will almost definitely see the colored side come up, and quite certainly more than once.
The example in the film would only be appropriate if the election had one singe town or county with 100 precincts. It is a gross misrepresentation of how the random audits would work.
The movie also makes a presumption at the end, that if you do find a brown peg, it doesn't accomplish anything because there are still 4 other brown pegs in there and no one knows. This is also not correct because most proposals I've seen call for a larger manual audit if a discrepancy is found. In other words, if a brown peg is found, then half, or even all the precincts in that county or town have to be audited. So the chances of finding the other ones are pretty good.
Having said all that, notice that in my formula for secure elections I did not specify the percentage required for the random audits. That is because I am not a statistician. I think the answer is somewhere in the middle and I would trust a team of statisiticians to come up with a reasonable amount to audit.
What you're looking for is a percentage that makes it almost certain to find the brown pegs, even if there was only a small number of them. In other words, go back to the example in the movie. the flaw again is the test is only done once. in reality on election night the exact same test is done thousands of times because there are probably tens of thousands of precincts across the country. I think most people would agree, if they did the exact same experiment in the movie 1,000 times, they would pick some brown pegs, even with 5% audits it would be almost certain. Actually even with just 2% audits, if they did it 1,000 times, chances are pretty good they would pick brown pegs, and probably several times it would happen. Of course the more you audit, the greater the chance of finding the brown pegs. The statisictians need to come up with a figure that makes it very likely to find the brown pegs.
What does it take? Can be done with audits of 2%, 5%, 10%... I don't know. But I don't think a statistician would agree that the movie is a good representation of how audits would or wouldn't catch fraud in an election. The problem again, is they only did it one time. If that were a fair representation - our elections just involved one county with 100 precincts for example, then I agree 100%, that just auditing 2 or 5% of the precincts would not be acceptable. In fact if that were the case I would be an advocate of 100% hand counts.
but that's not the case. in reality the experiment would be repeated over and over again and they would pick some brown pegs. and when they pick them they would have to then count a larger sample, or even the whole county, and they would find the other pegs too.
NOW.. the other comment is well taken. that auditing on the precinct level is somewhat of a problem. it would be better to audit each machine. I agree with that. but that adds another level of complication because whatever level you audit, you also have to make available the totals. in other words, if you audit at the machine level, you need to make available the totals for every machine so that observers (the public) can add them up, and verify each precinct total is actually the sum of all the machines in the precinct. This may or may not be worth the extra effort. It all comes down to the math. The chances of catching fraud under every scenario can be calculated and compared, as well they should.
I do not think it is possible to audit every machine, based on a certain percentage of the votes in each machine. I've heard people suggest a few ways to do this, but none have made complete sense to me. At the end of the day you have a stack of VVPATS and you know the total for the machine. I don't see how you can take a percentage of the VVPATS out of the stack and check something in the machine against it. If the machine only tells you the totals that it counted, the only thing you can do is count all the VVPATs for that machine and verify that is the total that the machine counted. If you are going to do that with every machine, you are then counting all the ballots by hand.
It really all comes down to math. We need to put some faith in mathmeticians. If they say there would be a 98% chance of catching fraud, would you be happy with that?
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