A Model of Non-Belief in the Law of Large Numbers

People believe that, even in very large samples, proportions of binary signals might depart significantly 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 might be determined by a rate different than the true rate.  In prediction, a non-believer expects the distribution of signals will have fat tails, more so for larger samples.  In inference, a non-believer remains uncertain and influenced by priors even after observing an arbitrarily large sample.  We explore implications for beliefs and behavior in a variety of economic settings.