Representativeness Biases and Lucky Store Effects

Abstract

Recent theories (Rabin, 2002; Rabin and Vayanos, 2010) propose that both the Gambler’s Fallacy and the Hot Hand Fallacy are driven by Representativeness Bias, also known as the Law of Small Numbers (Tversky and Kahneman, 1971). The Lucky Store Effect (Guryan and Kearney, 2008), in which the popularity of a lottery retailer surges after selling a winning ticket, bears an intuitive similarity to the Hot Hand Fallacy in terms of the belief that ‘previous winners will win again’, yet has been previously thought of as irreconcilable with Representativeness Bias. This paper develops theory and empirical evidence on this issue. We extend the Law of Small Numbers model of Rabin (2002), to the context where a decision-maker chooses among different lottery ticket stores after observing a history of prior outcomes. We show the conditions under which the decision-maker tends to believe that the store which has won previously has a higher chance of winning again, even if this event has only occurred once before. We then provide new empirical evidence on the Lucky Store Effect and Gambler’s Fallacy, from a large peer-to-peer online lottery marketplace for the Chinese national lottery. We find that lottery players exhibit Gambler’s Fallacy beliefs when picking lottery numbers, while believing in Lucky Stores when choosing which online lottery store to purchase their tickets from, which is consistent with the result in our model that decision-makers will tend to believe in the Lucky Store Effect when the perceived uncertainty about true probabilities is greater.