Inference by Believers in the Law of Small Numbers

Abstract

People exaggerate the degree to which small samples resemble the population from which they are drawn. To model this belief in the “Law of Small Numbers,” I assume that a person exaggerates the likelihood that a short sequence of i.i.d. signals resembles the long-run rate at which those signals are generated. Such a person believes in the “gambler's fallacy,” thinking that early draws of one signal increase the odds of next drawing other signals. When uncertain about the rate, the person overinfers from short sequences of signals that the rate is more extreme than it is, and consequently infers that there is more variation in these rates among different sources than there is. Economic applications are discussed, such as how the model predicts that investors will believe in nonexistent variation in the quality of mutual-fund managers.