The Pitfalls of Familiarity

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

something important to note about this kahneman/tversky system 1/2 stuff is you run the risk of walking away from it thinking that these things have a clear dividing line between them, as far as their fundamental nature and/or their applicability and/or their qualitative goodness/badness (primitive lizard/monkey/whatever vs enlightened patrician).

gerd gigerenzer, for instance, proposes that when we engage in what is popularly considered “rational thought”, we're reaching into a “toolbox” of multiple, individually fast-and-frugal heuristics, piling on more computational effort to solve a problem in more dimensions. additionally, wherever you stand on that theory, his experimental work demonstrates that just as easily as you can contrive a laboratory setting in which those heuristics are fallacious, you can contrive one in which they are beneficial; charitably you can interpret them as well-equipped to deal with uncertainty and incomplete information, and functioning as some sort of encoding of the ultimate likelihood of regression toward the mean

a fast heuristic can tell you the baseball bat costs one dollar or that it's likelier that linda is a bank teller and a feminist, sure, but slow, calculating thought is equally well-equipped to overfit to noise, rationalise an addiction, or send you down a detrimental neurotic spiral

anyway:

* cognition is wacky and quirky and difficult to poke and prod at under a microscope

* the jury is out on what kind of thought is most applicable in a given situation; good luck, buddy

* you should cultivate some degree of taste/discretion as to how hard you want to think about any given thing (one potential benchmark: are you accumulating a mile-long list of read-later bookmarks due to FOMO?)

* my two cents: someone who reads medium articles posted to hacker news is likely in minimal danger of under-employing system 2

I wonder if the error is more probable when there are no stakes.

For example, suppose aliens have captured Linda. They will only return her if you choose the description of her which has the best chance of being true.

Has anybody tested with something like that? I speculate that most people would instantly reject the answer with "extra stuff" in it. :)

People are tricked into thinking something improbable is more probable than it really is by coupling it with a separate, highly probable thing.

At first I thought this was just an obvious statistics thing, but it is psychological. You are distracted by the probable part of the combination and unless you think intentionally, are prone to make a mistake in how you perceive the combined probability.