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I got the question wrong because I misunderstood the options. I interpreted them as: 1. Linda is a bank teller and is not active in the feminist movement. 2.
by wavemode 3y ago
I got the question wrong because I misunderstood the options. I interpreted them as:
1. Linda is a bank teller and is not active in the feminist movement.
2. Linda is a bank teller and is active in the feminist movement.
If these were the options, then it's entirely possible for option 1 to be less likely than option 2. But the options are actually:
1. Either Linda is a bank teller and active in the feminist movement, or Linda is a bank teller and not active in the feminist movement.
2. Linda is a bank teller and is active in the feminist movement.
Framed this way, anyone can clearly see that option 1 cannot possibly be less likely than option 2, since option 1 includes option 2 as a possibility.
Indeed, even the Wikipedia article describing this problem[1] illustrates this very misconception:
> I am particularly fond of this example [the Linda problem] because I know that the [conjoint] statement is least probable, yet a little homunculus in my head continues to jump up and down, shouting at me—"but she can't just be a bank teller; read the description." - Stephen J. Gould
That homunculus in Gould's head seems to have misread the statements in exactly the same way. Nowhere in statement 1 does it say she is "just" a bank teller. But that's how it naturally reads to most people when placed next to statement 2.
Do most people have a poor understanding of conditional probability? Yes, of course. But I don't really buy that this "Linda problem" illustrates that.
[1]: https://en.wikipedia.org/wiki/Conjunction_fallacy https://en.wikipedia.org/wiki/Conjunction_fallacy
- xg15 3y agoYeah, had the same impression. The whole "fallacy" seems to be based on presenting the question in a misleading way. If the options had been: A) Linda is a bank teller and is also active in the feminist movement B) Linda is a bank teller, whether or not she is active in the feminist movement then I think more people would have realized that B contains A and is not a separate choice from a. The second point is that the criterion "linda is a bank teller" is actually superfluous, because there is no choice "linda is not a bank teller" and the probability is the same in all choices. At the same time, this is the only criterion for choice B. So if you factor out the "bank teller" term, the question becomes: Assume Linda had a history of social activism and is now a bank teller, which is more probable? A) Linda is active in the feminist movement B) Linda exists, I guess? So if presented unambiguously, the question actually becomes meaningless.
- stanfordkid 3y agoYeah exactly. It is non-sensical to say that she is a Bank Teller twice. English isn't mathematical syntax and directly converting a P(occupation=Bank Teller) => "Linda is a bank teller" is a bad translation of mathematical syntax to english, because we contextualize the statement when we are presented the next statement "Linda is a bank teller, and part of the feminist movement". Stupid stupid research IMO.