The evolution of superstition through optimal use of incomplete information

While superstitions appear maladaptive, they may be the inevitable result of an adaptive causal learning mechanism that simultaneously reduces the risk of two types of errors: the error of failing to exploit an existing causal relationship and the error of trying to exploit a nonexistent causal relationship. An individual’s exploration–exploitation strategy is a key component of managing this trade-off. In particular, on any given trial, the individual must decide whether to give the action that maximizes its expected fitness based on current information (exploit) or to give the action that provides the most information about the true nature of the causal relationship (explore). We present a version of this ‘two-armed bandit’ problem that allows us to identify the optimal exploration–exploitation strategy, and to determine how various parameters affect the probability that an individual will develop a superstition. We find that superstitions are more likely when the cost of the superstition is low relative to the perceived benefits, and when the individual’s prior beliefs suggest that the superstition is true. Furthermore, we find that both the total number of learning trials available, and the nature of the individual’s uncertainty affect the probability of superstition, but that the nature of these effects depends on the individual’s prior beliefs.