here is an edited selection from wikipedia for posterity:
Mathematically, the fallacy results from misunderstanding the concept of a conditional probability, which is defined as the probability that an event A occurs given that event B is known – or assumed – to have occurred, and it is written as
P(A|B).
The error is based on assuming that P(A|B) = P(B|A).
For example, let A represent the event of getting a haircut, and B the event of reading a haircut meme.
But this equality is not true: in fact, although P(A|B) is usually very small, P(B|A) may still be much higher.
No I don’t think that’s it. I would express it this way.
The chance of me reading a haircut meme straight after getting a haircut is near zero. But there are multiple people reading the haircut meme. So if you post a haircut meme, there is a high chance that ANY ONE of the readers will be straight after getting a haircut.
Like Sally Clark was convicted because the chance of having two miscarriages in a row is a million to one - it’s not plausible. The only other explanation is that she murdered her babies, so that’s the only plausable explanation.
But in a population of 60 million people, you are likely to find someone (or 60 people) who have had two miscarriages in a row. She was just the unlucky one.
Wikipedia has more detail and intersting angles, like the defendent’s fallacy, why it is a fallacy and when it might be correct.
Then there’s more stuff, and what happened after the conviction… That pathologist was never even charged with a crime, or lynched.
edit:
But your point is interesting too. The chance of winning the lottery given that I’ve just had a coffee is very low. But the chance that I’ve just had a coffee given that I’ve won the lottery is very high. But if I drink a coffee and then immediately win the lottery, people might assume that having just had a coffee improves my lottery chances.
I don’t know if there is a name for that one, but it sounds like something people do a lot.
I get sick, take medicine, get better. Then chance of having taken medicine given that I get better is 100%. So people will assume the medicine helps. But the chance that I get better given that I’ve taken medicine might be 10%. The chance I get better if I had not taken medicine might be more than 10%, but that result is not obvious at all.
Ah your explanation clears it up. That whole conditional probability thing is in the wikipedia article, but I see now that my explanation of the haircut thing was not correct.
I guess maybe this is a better formulation:
p1 = P(not being guilty | evidence found)
vs
p2 = P(evidence found)
Prosecutor’s fallacy would assert that, if p2 is small say 0.01%, then the defendent is guilty. But really the relevant probability is p1, which could be quite a bit larger than 0.01%.
it’s not so easy to explain. look up Wikipedia, or even better look up Sally Clark. she’s the textbook example, and an amazing story anyway.
pretty interesting, thx.
here is an edited selection from wikipedia for posterity:
Mathematically, the fallacy results from misunderstanding the concept of a conditional probability, which is defined as the probability that an event A occurs given that event B is known – or assumed – to have occurred, and it is written as P(A|B).
The error is based on assuming that P(A|B) = P(B|A).
For example, let A represent the event of getting a haircut, and B the event of reading a haircut meme.
But this equality is not true: in fact, although P(A|B) is usually very small, P(B|A) may still be much higher.
No I don’t think that’s it. I would express it this way.
Like Sally Clark was convicted because the chance of having two miscarriages in a row is a million to one - it’s not plausible. The only other explanation is that she murdered her babies, so that’s the only plausable explanation.
But in a population of 60 million people, you are likely to find someone (or 60 people) who have had two miscarriages in a row. She was just the unlucky one.
Wikipedia has more detail and intersting angles, like the defendent’s fallacy, why it is a fallacy and when it might be correct.
Then there’s more stuff, and what happened after the conviction… That pathologist was never even charged with a crime, or lynched.
edit:
But your point is interesting too. The chance of winning the lottery given that I’ve just had a coffee is very low. But the chance that I’ve just had a coffee given that I’ve won the lottery is very high. But if I drink a coffee and then immediately win the lottery, people might assume that having just had a coffee improves my lottery chances.
I don’t know if there is a name for that one, but it sounds like something people do a lot.
I get sick, take medicine, get better. Then chance of having taken medicine given that I get better is 100%. So people will assume the medicine helps. But the chance that I get better given that I’ve taken medicine might be 10%. The chance I get better if I had not taken medicine might be more than 10%, but that result is not obvious at all.
Ah your explanation clears it up. That whole conditional probability thing is in the wikipedia article, but I see now that my explanation of the haircut thing was not correct.
I guess maybe this is a better formulation:
p1 = P(not being guilty | evidence found)
vs
p2 = P(evidence found)
Prosecutor’s fallacy would assert that, if p2 is small say 0.01%, then the defendent is guilty. But really the relevant probability is p1, which could be quite a bit larger than 0.01%.
Anyways let me know if you agree lol.