Linda is a bank teller: This first puzzle is a classic.

It's from a 1983 research study on how people think about probability.

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

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I think this is a far better explanation. The long hand is clear and the reference to Tversky and Kahnema is helpful. It should be given here anyway:- The conjunction fallacy is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one.

from:-

Linda and the Conjunction Fallacy 02/21/17 on Random

https://mxbu.github.io/logbook/2017/02/21/conjunction-fallacy/ The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman:

The majority of those asked chose option 2. However, the probability of two events occurring together (in “conjunction”) is always less than or equal to the probability of either one occurring alone—formally, for two events A and B this inequality could be written as

P(A∩B)≤P(A) and P(A∩B)≤P(B)

For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = 0.05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = 0.95, then, assuming independence, Pr(Linda is a bank teller and Linda is a feminist) = 0.05 × 0.95 or 0.0475, lower than Pr(Linda is a bank teller).

Tversky and Kahneman argue that most people get this problem wrong because they use a heuristic (an easily calculated procedure) called representativeness to make this kind of judgment: Option 2 seems more “representative” of Linda based on the description of her, even though it is clearly mathematically less likely.

#Combinatorics

Note by Adam Saltiel
1 year, 5 months ago

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