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From a formal logic perspective, the answer is obviously the first. Yet many people, because of the information about Linda's behavior and outlook on life, choose the second. in his book [Gut Feelings: The Intelligence of the Unconscious], Gerd Gigerenzer points out that the reason for the confusion about the conjunction "and" is that a natural language does not work the way of logic. His first example to illustrate the discrepancy is | From a formal logic perspective, the answer is obviously the first. Yet many people, because of the information about Linda's behavior and outlook on life, choose the second. in his book [http://www.amazon.com/Gut-Feelings-Intelligence-Gerd-Gigerenzer/dp/0143113763 Gut Feelings: The Intelligence of the Unconscious], Gerd Gigerenzer points out that the reason for the confusion about the conjunction "and" is that a natural language does not work the way of logic. His first example to illustrate the discrepancy is | ||
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*Peggy and Paul married and Peggy became pregnant. | *Peggy and Paul married and Peggy became pregnant. | ||
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His empirical claim is that people easily figure things out with this rephrasing. | His empirical claim is that people easily figure things out with this rephrasing. | ||
Submitted by Paul Alper | |||
'''Note''': An earlier Chance News item [http://test.causeweb.org/wiki/chance/index.php/Chance_News_68 Stories and st] John Allen Paulos's take on the Linda Problem | |||
Revision as of 00:27, 17 November 2013
The Linda Problem
The Linda Problem is a Kahneman and Tversky's famous illustration of the conjuction fallacy:
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. Which is of the following is more probable?
- Linda is a bank teller.
- Linda is a bank teller and is active in the feminist movement.
From a formal logic perspective, the answer is obviously the first. Yet many people, because of the information about Linda's behavior and outlook on life, choose the second. in his book Gut Feelings: The Intelligence of the Unconscious, Gerd Gigerenzer points out that the reason for the confusion about the conjunction "and" is that a natural language does not work the way of logic. His first example to illustrate the discrepancy is
- Peggy and Paul married and Peggy became pregnant.
- Peggy became pregnant and Peggy and Paul married.
His second example is
- Mark got angry and Mary left.
- Mary left and Mark got angry.
Obviously, either of the above violates Prob (A and B) = Prob (B and A). The following does not violate Prob (A and B) = Prob (B and A):
- Verona is in Italy and Valencia is in Spain.
- Valencia is in Spain and Verona is in Italy.
Further,
Even more surprising, we also know without thinking when and should be interpreted as the logical [inclusive] or, as in the sentence
- We invited friends and colleagues.
One of Gigerenzer's continuing themes is that instead of probability we should concentrate on frequency, which is much easier to understand. He would rephrase Linda to
There are a hundred persons who fit the description above (i.e., Linda's). How many of them are
- bank tellers?
- bank tellers and active in the feminist movement?
His empirical claim is that people easily figure things out with this rephrasing.
Submitted by Paul Alper
Note: An earlier Chance News item Stories and st John Allen Paulos's take on the Linda Problem