Conjunction Fallacy
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[edit] Definition
The conjunction fallacy is an informal logical fallacy, where a participant believes that a conjunctive statement is more likely than any of its components.
This is a fallacy because it is mathematically impossible for such a situation to hold.
[edit] Examples
Example 1[after (Tversky and Kahnemann, 1983)] :
- Protagonist: 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 antinuclear demonstrations.
- Antagonist: Yeah, and?
- Protagonist: So which is more likely to be true, A), that Linda is a bank teller, or B) that Linda is a bank teller and is active in the feminist movement?
- Antagonist: Well, with a background like that, she's almost got to be a feminist, so I would go with B. [1]
In the original T&K experiments, more than 50% of the participants judged the second statement (B) to be more likely than the first, despite the fact that that is mathematically impossible. They most likely assumed that the first statement (A) means that Linda is a bank teller but is not active in the feminist movement, when in fact it says no such thing.
Example 2 [after (Sides, et al., 2001)]:
- Protagonist: Which of the following do you think is more likely to happen: A) that a tax cut will be passed between Jan 1 and Mar 31, 2006, or that B) a tax cut will be passed between Jan 1 and Mar 31, 2006 with the support of most Republicans?
- Antagonist: Well, there's no way a tax cut could pass without the support of most Republicans, so again, I pick B.
[edit] Exceptions to the Rule
In normal human conversation, a choice between "A" or "A and B" would be tautological from a logical standpoint, which, on its face violates a rule of conversation[2]. It is common for the listener to subconsciously re-interpret the first choice as "A and not B", as the intended meaning, and in many cases, this is the intended interpretation.
Using pure logic within this conversational style would be considered absurd:
- P: What do you think? Will Saddam just sit there today or will he have another outburst?
- A: Huh? If he has an outburst or not, he'll be sitting there in any case. Obviously, the less determined event is more likely.
[edit] Related Articles
[edit] References
- Sides, A, Osherton, D., Bonini, N., Viale, R. (2001). "On the reality of the conjunction fallacy.
- Tversky, A. and Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90:293-315.
