Sunday, October 24, 2010

The Conjunction Fallacy

The foibles of human credibility always entertain me. Sure I fall for them too, but at least I try to be aware of them and limit my mistakes. The tragedy is that there are a lot of people who simply refuse to recognize the limits of their intelligence and the extent of their credulity.

Here's a bit from an article published in the NY Times on the Opinionator blog, a blog for philosophers and their ideas. This article is by the mathematician John Allan Paulos:
The so-called “conjunction fallacy” suggests another difference between stories and statistics. After reading a novel, it can sometimes seem odd to say that the characters in it don’t exist. The more details there are about them in a story, the more plausible the account often seems. More plausible, but less probable. In fact, the more details there are in a story, the less likely it is that the conjunction of all of them is true. Congressman Smith is known to be cash-strapped and lecherous. Which is more likely? Smith took a bribe from a lobbyist or Smith took a bribe from a lobbyist, has taken money before, and spends it on luxurious “fact-finding” trips with various pretty young interns. Despite the coherent story the second alternative begins to flesh out, the first alternative is more likely. For any statements, A, B, and C, the probability of A is always greater than the probability of A, B, and C together since whenever A, B, and C all occur, A occurs, but not vice versa.

This is one of many cognitive foibles that reside in the nebulous area bordering mathematics, psychology and storytelling. In the classic illustration of the fallacy put forward by Amos Tversky and Daniel Kahneman, a woman named Linda is described. She is single, in her early 30s, outspoken, and exceedingly smart. A philosophy major in college, she has devoted herself to issues such as nuclear non-proliferation. So which of the following is more likely?

a.) Linda is a bank teller.

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

Although most people choose b.), this option is less likely since two conditions must be met in order for it to be satisfied, whereas only one of them is required for option a.) to be satisfied.

(Incidentally, the conjunction fallacy is especially relevant to religious texts. Imbedding the God character in a holy book’s very detailed narrative and building an entire culture around this narrative seems by itself to confer a kind of existence on Him.)
That last bit about religious credulity should ring home with lots of people. But it doesn't. Most of them simply refuse to accept modern science and the understanding of the human mind's cognitive illusions and errors.

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