Minimal representations of possibility at age 3

Young children do not always consider alternative possibilities when planning. Suppose a prize is hidden in a single occluded container and another prize is hidden in an occluded pair. If given a chance to choose one container and receive its contents, choosing the singleton maximizes expected reward because each member of the pair might be empty. Yet, 3-y-olds choose a member of the pair almost half the time. Why don't they maximize expected reward? Three studies provide evidence that 3-y-olds do not deploy possibility concepts like MIGHT, which would let them represent that each container in the pair might and might not contain a prize. Rather, they build an overly specific model of the situation that correctly specifies that the singleton holds a prize while inappropriately specifying which member of the pair holds a prize and which is empty. So, when asked to choose a container, they see two equally good options. This predicts approximately 50% choice of the singleton, observed in studies 1 and 3. But when asked to throw away a container so that they can receive the remaining contents (study 2), they mostly throw away a member of the pair. The full pattern of data is expected if children construct overly specific models. We discuss whether 3-year-olds lack possibility concepts or whether performance demands prevent deployment of them in our tasks.