A Hierarchical Cognitive Threshold Model of Human Decision Making on Different Length Optimal Stopping Problems

In optimal stopping problems, people are asked to choose the maximum out of a sequence of values, under the constraint that a number can only be chosen when it is presented. We present a series of threshold models of human decision making on optimal stopping problems, including a new hierarchical model that assumes individual differences in threshold setting are controlled by deviations or biases from optimality associated with risk propensity, and is applicable to optimal stopping problems of any length. Using Bayesian graphical modeling methods, we apply the models to previous data involving 101 participants with large individual differences who completed sets of length 5 and length 10 problems. Our results demonstrate the effectiveness of the bias-from-optimal hierarchical model, find individual differences in thresholds that people use, but also find that these individual differences are stable across the two optimal stopping tasks.