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1/ When the FBI says that it “found no evidence” that votes were changed in the 2016 election, it is VERY important that the media specify that the FBI found no FORENSIC evidence. But forensic evidence, such as the presence of malware, represents just one type of evidence.
2/ Seth Abramson @SethAbramson already did a brilliant job of illuminated the difference between DIRECT evidence and CIRCUMSTANTIAL evidence @Maddow @RepCummings @RepJerryNadler @tedlieu @AOC
3/ It is now time to discuss the STATISTICAL evidence that votes were changed in 2016; this evidence is unique from both forensic and circumstantial evidence. H/t to @saill and votesleuth.org for incredible work. The findings are simply too important not to spread wide!
4/ Webster’s defines statistics as “a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data.” Stat relies on two things: (1) data and (2) assumptions that the data comes from a particular data generating process
5/ The outcome of a fair coin toss, for example, is presumed to derive from what is called a Bernoulli process, which has a distribution that yields only dichotomous outcomes of tails [0] or heads [1].
6/ There are many other probability distributions out there that are used for all sorts of things, such as predicting when food will spoil (so as to place expiration dates on food) or how long a smoker will live if obese.
7/ One of the most powerful rules in statistics (actually it’s a theorem) is known as a Law of Large Numbers. Essentially, the Law of Large Numbers says that if you flip a fair coin enough times, the number of heads that will appear should be 1/2 of all the outcomes.
8/ Is it possible to flip a fair coin 10 times and get 10 heads in a row? Absolutely! Is it possible to flip a fair coin 100,000 times and get 100,000 heads in a row? The Law of Large Numbers says no. Not if it is a FAIR coin.
9/ At that number of flips, the empirical probability of a given outcome (the number of heads observed) should equal the theoretical probability of a given outcome (50:50 for a fair coin for both heads and tails). And this is really important to remember....
10/ Here is what that looks like for a fair coin toss. It is clear there are streaks one way or other, but in the end, cumulatively with enough flips, you should end up near 50:50. 
11/ So what happens if you have a weighted coin? You should see the same pattern, only the theoretical probability should be biased in favor of one side or the other. It might look something like this:
12/ So what happens if you flip two coins at the same time? When one coin is fair (50:50) and one coin is very unfair (90:10), the pattern will look like this:
13/ That’s pretty much identical to when you had just one biased coin. But what happens if you add the flip outcomes together separately, first from the fair coin, then second from the biased coin?
14/ Boom! Now we have something! @maddow The fair coin obviously will converge on the 50:50 mark with sufficient numbers of tosses, but adding the biased coin suddenly changes the direction of the convergence.
15/ The fact that is no longer flat at a high number of tosses is an indication that you have two different distributions, one centered on one level and the other centered on another level.
16/ Why does this matter for election watching? Because as precinct data comes in one after another, each new precinct is adding coin tosses into the total pool of outcomes.
17/ Candidate A may win one precinct 55%-45% and lose another 43%-57%. But if the true proportion of support across all precincts is 53%-47%, then over time, the outcome has to converge somewhere around 53% for Candidate A.
18/ So let’s assume we want to show statistical evidence that vote flipping occurred. To do that, we must isolate all untampered precincts then add in the tampered precincts. If they are randomly mixed, we won’t see the convergence, then the change in convergence (see 15/ above)
19/ So which precincts might be tampered with? Obviously, it would be stupid for a hacker to flip 100% of votes in certain precincts to benefit a favored candidate. Everyone would see something was amiss.
20/ So rather than doing that, a crafty hacker should want to flip just a few votes here and there so that the total vote count yields the desired outcome across all precincts cumulatively.
21/ @saill and votesleuth.org argue the best way to do that is to flip votes in LARGER precincts, so they become lost in the noise. Because TV announcers just want to point out who won what precinct and by how many votes, no one pays attention to precise breakdowns.
22/ If you take all the election precincts, and add in the ratio of votes for each precinct one at a time (like the coin flips we cumulated earlier), we should be able to spot vote flipping if we can isolate all the non-tampered precincts. @saill recommends isolating by size.
23/ This is what @SteveKornacki should do in 2020. Are you listening @Maddow? As an example, here is Forsyth County, North Carolina. This is a clear indication of vote flipping that shows two different "coins"--one fair and one weighted. The hacker is the weighted coin here.
24/ And here’s Duval County, Florida. Notice the Democratic registration compared to the final vote. This cannot happen if the vote is fair because there is only one distribution. This is what the media missed by trying to explain Trump's votes as some sort of "Bradley effect."
25/ And here is Burks County, PA. While the FBI may not have found forensic evidence of vote flipping, these three charts show clear STATISTICAL EVIDENCE of vote flipping. The Law of Large Numbers does not lie. Thanks to @saill and votesleuth.org! Keep up the good work!
