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Conjunction fallacy
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Conjunction fallacy
A conjunction effect or Linda problem is a bias or mistake in reasoning where adding extra details (an "and" statement or logical conjunction; mathematical shorthand: ) to a sentence makes it appear more likely. Logically, this is not possible, because adding more claims can make a true statement false, but cannot make false statements true: If A is true, then might be false (if B is false). However, if A is false, then will always be false, regardless of what B is. Therefore, cannot be more likely than A.
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."
The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman:
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 more probable?
The majority of those asked chose option 2. However, this is logically impossible: if Linda is a bank teller active in the feminist movement, then she is a bank teller. Therefore, it is impossible for 2 to be true while 1 is false, so the probabilities are at most equal.
More generally, the probability of two events occurring together (that is, in conjunction) is always less than or equal to the probability of either one occurring itself. For two events A and B this inequality can be written as .
For example, even choosing a very low probability of Linda's 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 these two facts are independent of each other, 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).
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Conjunction fallacy
A conjunction effect or Linda problem is a bias or mistake in reasoning where adding extra details (an "and" statement or logical conjunction; mathematical shorthand: ) to a sentence makes it appear more likely. Logically, this is not possible, because adding more claims can make a true statement false, but cannot make false statements true: If A is true, then might be false (if B is false). However, if A is false, then will always be false, regardless of what B is. Therefore, cannot be more likely than A.
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."
The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman:
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 more probable?
The majority of those asked chose option 2. However, this is logically impossible: if Linda is a bank teller active in the feminist movement, then she is a bank teller. Therefore, it is impossible for 2 to be true while 1 is false, so the probabilities are at most equal.
More generally, the probability of two events occurring together (that is, in conjunction) is always less than or equal to the probability of either one occurring itself. For two events A and B this inequality can be written as .
For example, even choosing a very low probability of Linda's 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 these two facts are independent of each other, 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).