Cognitive models of optimal sequential search with recall

Many everyday decisions require sequential search, according to which available choice options are observed one at a time, with each observation involving some cost to the decision maker. In these tasks, decision makers need to trade-off the chances of finding better options with the cost of search. Optimal strategies in such tasks involve threshold decision rules, which terminate the search as soon as an option exceeding a reward value is found. Threshold rules can be seen as special cases of well-known algorithmic decision processes, such as the satisficing heuristic. Prior work has found that decision makers do use threshold rules, however the stopping thresholds observed in data are typically smaller than the (expected value maximizing) optimal threshold. We put forward an array of cognitive models and use parametric model fits on participant-level search data to examine why decision makers adopt seemingly suboptimal thresholds. We find that people's behavior is consistent with optimal search if we allow participants to display risk aversion, psychological effort cost, and decision error. Thus, decision makers appear to be able to search in a resource-rational manner that maximizes stochastic risk averse utility. Our findings shed light on the psychological factors that guide sequential decision making, and show how threshold models can be used to describe both computational and algorithmic aspects of search behavior.