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Encyclopedia > Conjunction fallacy

The conjunction fallacy is a logical fallacy that occurs when it is assumed that specific conditions are more probable than general ones. A logical fallacy is an error in logical argument which is independent of the truth of the premises. ...


The most oft-cited example of this fallacy originated with Amos Tversky and Daniel Kahneman: Amos Tversky (March 16, 1937 - June 2, 1996) was a pioneer of cognitive science, a longtime collaborator of Daniel Kahneman, and a key figure in the discovery of systematic human cognitive bias and handling of risk. ... Daniel Kahneman (born 1934 in Tel Aviv, Israel) is a key pioneer and theorist of behavioral finance, which integrates economics and cognitive science to explain seemingly irrational risk management behavior in human beings. ...

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 likely?
  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, mathematically, the probability of two events occurring together (in "conjunction") will always be less than or equal to the probability of either one occurring alone. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... The word probability derives from the Latin probare (to prove, or to test). ...


In mathematical notation, this inequality could be written for two events A and B as In probability theory, Booles inequality (also known as the union bound) says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. ...

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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).


Tversky and Kahneman argue that most people get this problem wrong because they use the representativeness heuristic 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. The representative heuristic is a heuristic first identified by Amos Tversky and Daniel Kahneman. ...


Many other demonstrations of this error have been studied. In another experiment, for instance, policy experts were asked to rate the probability that the Soviet Union would invade Poland and the United States would break off diplomatic relations, all in the following year. They rated it on average as having a 4% probability of occurring. Another group of experts was asked to rate the probability simply that the United States would break off relations with the Soviet Union in the following year. They gave it an average probability of only 1%. Researchers argued that a detailed, specific scenario seemed more likely because of the representativeness heuristic, but each added detail would paradoxically make the scenario less and less likely. In this way it could be similar to the misleading vividness or slippery slope fallacies. Also, some of those questioned probably confused the question to "if Soviet Union conquered...". This page is about negotiations; for the board game, see Diplomacy (game). ... The representative heuristic is a heuristic first identified by Amos Tversky and Daniel Kahneman. ... Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines do not exist. ... The logical fallacy of misleading vividness involves describing some occurrence in vivid detail, even if it is an exceptional occurrence, to convince someone that it is a problem. ... In the contexts of debate or of rhetoric, the phrase slippery slope, also appearing as the thin end of the wedge or the camels nose, refers both to an argument about the likelihood of one event given another, and to a fallacy about the inevitability of one event given...


References

  • Tversky, A. and Kahneman, D. (1983). Extension versus intuititve reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.
  • 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.

  Results from FactBites:
 
The Fallacy Files Glossary (2304 words)
This glossary defines logical terms used in the files on individual fallacies and in entries in the weblog.
For instance, an ambiguous or vague sentence is not in and of itself fallacious, since it is not an argument, but it may cause somebody to infer a false conclusion.
A wild example of a fallacy is one found in the natural habitat of fallacious arguments, namely, the reasoning of real people, as opposed to the exercises in a logic textbook.
  More results at FactBites »

 
 

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