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conjunction fallacy : ウィキペディア英語版
conjunction fallacy
The conjunction fallacy is a formal fallacy that occurs when it is assumed that specific conditions are more probable than a single general one.
The most often-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman:〔Tversky, A. and Kahneman, D. (1982) "Judgments of and by representativeness". In D. Kahneman, P. Slovic & A. Tversky (Eds.), ''Judgment under uncertainty: Heuristics and biases''. Cambridge, UK: Cambridge University Press.〕〔

''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?


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

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 \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) = 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.
In other demonstrations they argued that a specific scenario seemed more likely because of representativeness, but each added detail would actually make the scenario less and less likely. In this way it could be similar to the misleading vividness or slippery slope fallacies. More recently Kahneman has argued that the conjunction fallacy is a type of extension neglect.〔Kahneman, Daniel. (2000). "Evaluation by moments, past and future". In Daniel Kahneman and Amos Tversky (Eds.). ''Choices, Values and Frames.''〕
==Joint versus separate evaluation==

In some experimental demonstrations the conjoint option is evaluated separately from its basic option. In other words, one group of participants is asked to rank order the likelihood that Linda is a bank teller, a high school teacher, and several other options, and another group is asked to rank order whether Linda is a bank teller and active in the feminist movement versus the same set of options (without Linda is a bankteller as an option). In this type of demonstration different groups of subjects rank order Linda as a bank teller and active in the feminist movement more highly than Linda as a bank teller.〔
Separate evaluation experiments preceded the earliest joint evaluation experiments, and Kahneman and Tversky were surprised when the effect was still observed under joint evaluation.
In separate evaluation the term conjunction effect may be preferred.〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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