Model-based wisdom of the crowd for sequential decisions

We use cognitive models to apply the wisdom of the crowd to three sequential decision making problems: bandit problems, optimal stopping problems, and the Balloon Analogue Risk Task (BART). In each of these problems, people make a sequence of choices under uncertainty, with individual differences in decision making that depend on different attitudes toward risk. Each of the problems also has a known optimal decision-making strategy. Standard methods for the wisdom of the crowd, based on taking the modal behavior, are generally not applicable to these problems, because of their sequential nature. For example, the state-space of a bandit problem can be so large that, even for a large crowd of people, there will be game states that no individual encountered, and so there is no behavior to aggregate. We solve this problem using cognitive models, and inferring individual-level parameter values that predict what each individual would do for each sequential decision. The mode of these model-based predicted decisions then defines a crowd decision whose performance can be compared to individual and optimal performance.