This article describes an experiment that shows that rational people can be deluded into believing that random events are not random. Subjects who correctly predicted the result of a coin toss, are more willing to bet on the result of subsequent coin tosses. They become more willing as the number of successful calls increases.
This may explain why investors are so willing to bet on tips, and pay for financial advice, in a stock market that is more random than people would like to believe. It also calls to question the dominant macroeconomic theory that assumes purely rational choices by agents with perfect information.
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