Understand the conjunction fallacy (the Linda problem) and tie together all the “probability” biases of the unit.
The Linda problem
Conjunction fallacy
Another famous experiment by Kahneman and Tversky. The description: “Linda is 31, smart, outspoken, and majored in philosophy. As a student she cared about justice and discrimination and went to demonstrations.”
The question: which is more likely?
(1) Linda is a bank teller.
(2) Linda is a bank teller AND active in the feminist movement.
Most people choose (2) — the image of an “activist” fits the description so well. But that's logically impossible: option (2) is part of option (1). The group “bank tellers who are activists” lies entirely inside the group “bank tellers”. Two conditions together can't be MORE likely than one of them alone. So (1) is always at least as likely as (2).
This is the conjunction fallacy: adding a plausible detail (“activist”) makes the story more convincing to intuition but mathematically less likely, since every extra condition can only narrow the set.
The moral: a plausible, “neat” story is not the same as a likely one. The more colorful details a forecast has, the better it sounds and the less likely it really is.
Lesson notes
Conjunction fallacy
Another famous experiment by Kahneman and Tversky. The description: “Linda is 31, smart, outspoken, and majored in philosophy. As a student she cared about justice and discrimination and went to demonstrations.”
The question: which is more likely?
(1) Linda is a bank teller.
(2) Linda is a bank teller AND active in the feminist movement.
Most people choose (2) — the image of an “activist” fits the description so well. But that's logically impossible: option (2) is part of option (1). The group “bank tellers who are activists” lies entirely inside the group “bank tellers”. Two conditions together can't be MORE likely than one of them alone. So (1) is always at least as likely as (2).
This is the conjunction fallacy: adding a plausible detail (“activist”) makes the story more convincing to intuition but mathematically less likely, since every extra condition can only narrow the set.
The moral: a plausible, “neat” story is not the same as a likely one. The more colorful details a forecast has, the better it sounds and the less likely it really is.