A Model of Non-Belief in the Law of Large Numbers Draft for distribution in February 2011 talks | Missing proofs

Abstract

Psychological research suggests that people believe that even in very large samples proportions might depart signicantly from the population mean. We model this \non-belief in the Law of Large Numbers by assuming that a person believes that proportions in any given sample of binary signals might be determined by a rate dierent than the true rate. In inference, a non-believer attends too little to sample size, and remains uncertain even after observing an arbitrarily large sample. Non-belief is often a necessary enabler of other biases, such as the over-inuence of vivid signals, that would otherwise be overwhelmed by the logic of the Law of Large Numbers. Because it prevents recognition that a large number of independent betterthan-fair bets is extremely unlikely to yield an aggregate loss, non-belief helps explain how loss aversion can induce reluctance to accept even negligible risk. We explore various assumptions about whether non-believers separately or jointly process signals that arrive in separate clumps. If a non-believer naively anticipates separating new signals but after the fact infers by pooling all signals, he can be caught in a \learning trap| persistently paying for information that he thinks will let him reach a decision, but which in retrospect he nds inconclusive. In observational-learning settings, non-believers can end up in an information cascade where they ignore their private information, but (unlike believers) may also end up in an \informational eddy, forever following their own signals.

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