Conjunction fallacy


 
Name of fallacy Conjunction fallacy
Aliases  
Type Deductive Argument, Formal Argument
Description Occurs when it is assumed that specific conditions are more probable than a single general one.
Example The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman:[1]

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?

       1. Linda is a bank teller.
       2. Linda is a bank teller and is active in the feminist movement.

85% 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
FormFor two events A and B this inequality could be written as \Pr(A \and B) \leq \Pr(A), and \Pr(A \and B) \leq \Pr(B).
For example, even choosing a very low probability of Linda being a bank teller, say Pr(Linda is a bank teller) = .05 and a high probability that she would be a feminist, say Pr(Linda is a feminist) = .95, then, assuming independence, Pr(Linda is a bank teller AND Linda is a feminist) = .05 × .95 or .0475, lower than Pr(Linda is a bank teller).
Treatment This is a mathematical error. The probability of two events occurring together (in "conjunction") is always less than or equal to the probability of either one occurring alone. This can be proven mathematically and by showing this the fallacy can be dealt with.

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