Belief in the Law of Small Numbers" teased out the implications of a single mental error that people commonly made-even when those people were trained statisticians. People mistook even a very small part of a thing for the whole. Even statisticians tended to leap to conclusions from inconclusively small amounts of evidence. They did this, Amos and Danny argued, because they believed-even if they did not acknowledge the belief-that any given sample of a large population was more representative of that population than it actually was. The power of the belief could be seen in the way people thought of totally random patterns-like, say, those created by a flipped coin. People knew that a flipped coin was equally likely to come up heads as it was tails. But they also thought that the tendency for a coin flipped a great many times to land on heads half the time would express itself if it were flipped only a few times-an error known as "the gambler's fallacy." People seemed to believe that if a flipped coin landed on heads a few times in a row it was more likely, on the next flip, to land on tails-as if the coin itself could even things out. "Even the fairest coin, however, given the limitations of its memory and moral sense, cannot be as fair as the gambler expects it to be," they wrote. In an academic journal that line counted as a splendid joke.
( Michael Lewis )
[ The Undoing Project: A ]
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