SaidNobody wrote: ↑Fri Jan 15, 2021 11:45 am
But altogether and among many others, it is sort of like one in 15 quadrillion chance that Joe Biden won. I admit, I did not run those stats myself.
The 15 quadrillion chance is a calculation based on a terrible model of votes. In particular, it assumes the distribution of presidential votes doesn't change throughout the election. That's a garbage assumption
that the calculation is very sensitive to. Stop using this figure. Stop, stop, stop. It's a bullshit statistic.
Stop.
Stop.
Stop.
Stop. It hurts the stats center of my brain to see it. Toss it out of your head. Remove it from your list of talking points. We've been over it before, and I said the same thing then.
Now, I do recognize that you're drawing an analogy.
The fact that evidence is unlikely given a hypothesis doesn't make the hypothesis wrong. You're not accounting for the probability of such a huge conspiracy, which is ridiculously small. Every conspiracy theory has the same believability problem: the probability of it decreases exponentially with each added participant.
Math lesson time!
You're comparing P(Evidence | Conspiracy), the probability of the evidence given a massive nationwide conspiracy, with P(Evidence | No conspiracy). You say the first number is bigger, so there's a conspiracy. Let's say for the sake of argument that it is.
Those are the wrong numbers to compare. What we should compare are these, the probability that there's a massive nationwide conspiracy or not given the evidence.
P(Conspiracy | Evidence) = P(Conspiracy) * P(Evidence | Conspiracy) / P(Evidence)
P(No conspiracy | Evidence) = P(No conspiracy) * P(Evidence | No conspiracy) / P(Evidence)
(This is Bayes' law. Every statistician would tell you it's the right thing to use.)
Because P(Evidence) - the probability of seeing the evidence regardless of how it came to be - happens to be hard to calculate even when things are simple, it's nice that we can forget about it because it's the denominator in both formulas. We can compare these two probabilities, then:
P(Conspiracy) * P(Evidence | Conspiracy)
P(No conspiracy) * P(Evidence | No conspiracy)
The bigger one wins.
Where conspiracy theories run into trouble is in their
a priori unlikelihood. How probable is it that all of the participants can keep quiet? Never let something major slip? Never leave incriminating evidence lying around? Never leave an obvious trail to follow? Per-participant, these are roughly independent outcomes. So even if the probability for each is low, the chance that
at least one messes up is high. With thousands of participants, none of them messing up is like flipping a thousand coins and getting all heads. So P(Conspiracy) must be very low - and we're talking
actual 1-in-15-quadrillion probabilities here, or smaller.
Does that mean there isn't ever a massive conspiracy? No, but to conclude it rationally you need a pretty small P(Evidence | No conspiracy), which entails seeing evidence that basically can't be explained without the massive conspiracy.
All of the evidence is perfectly explainable. Some, like "Trump was winning when we went to bed but losing when we got up"
is actually very likely when evaluated using any reasonable model. Therefore, by incorporating P(Conspiracy), I arrive at P(No conspiracy | Evidence) as being vastly more likely than P(Conspiracy | Evidence).
I don't actually do that mental math - it's more like "I'll believe there's a massive conspiracy when I see some very strong evidence for one" or "extraordinary claims require extraordinary evidence" - but it's nice that the math justifies my intuition.