Sequential choices using signal detection theory can reverse classical predictions

The behavioural sciences have been strongly influenced for several decades by signal detection theory (also known as "error management theory" and "ROC analysis"). The theory provides simple logic about how individuals should behave in order to maximize their expected payoff in a single decision; for instance, the theory predicts that as the probability of a particular danger increases, individuals should be more prone to avoiding that danger. However, such findings need not hold in situations where more than 1 decision will be made, and recent work has shown that when behavior is allowed to depend on the energy reserves of the individual, the classical predictions can be reversed. Here, we use a simple analytic technique to show that even when the same behavioral rules are used at every reserve level, the predictions of classical signal detection theory (as though only a single decision will be made) are often reversed in a world where autocorrelation is high. The classical predictions are reversed because individuals will often make multiple decisions to achieve a goal, and the outcome of an action can influence the number of subsequent decisions that are required. The finding suggests that fundamental predictions should be altered across many of the behavioral sciences, not only in relation to signal detection theory, but also other single-decision models.