[dcow]

So if I find 10 people that claim, each with a 10% likelihood of being true, that the dark side of the moon has a scar that looks like Pikachu, then it’s 100% true?

That doesn’t make sense either. Seems like someone is falling prey to an intuitive fallacy of probability.

The weird model is just wrong in the first place. The commenter we’re discussing conflates the probability of two people saying something with the probability that what they say is true. So yes, you have to model the situation correctly in the first place.

[ironborn123]

No,even though the 10 pikachu fans assess independently, their estimations will be correlated. As you may already know the overall estimate wont be 100%, rather about 65%. The formula when the assessors are known to be independent, is simpler and has already been indicated by another commenter, P(A1 or A2 or A3 or ..An) = 1 - P(not A1)P(not A2)..P(not An)

On the other hand, if those 10 were engaged in complete groupthink (so no additional information beyond the first guy), the overall estimate would remain 10%.

In general, the answer would lie between 0.1 and ~0.65 depending on how their estimates influence each other.

[martindbp]

Of course you don't add probabilities, but for small probabilities it's an ok estimate. The chance of getting a single heads in N coin flips is one minus the probability of always getting tails, so 1-P(tails)^N. If P(heads) and N are small (e.g 0.1 and N=2), adding the probabilities is a perfectly reasonable estimate, just plug in the numbers and check for yourself.