A detailed comparison of optimality and simplicity in perceptual decision making

Two prominent ideas in the study of decision making have been that organisms behave near-optimally, and that they use simple heuristic rules. These principles might be operating in different types of tasks, but this possibility cannot be fully investigated without a direct, rigorous comparison within a single task. Such a comparison was lacking in most previous studies, because (a) the optimal decision rule was simple, (b) no simple suboptimal rules were considered, (c) it was unclear what was optimal, or (d) a simple rule could closely approximate the optimal rule. Here, we used a perceptual decision-making task in which the optimal decision rule is well-defined and complex, and makes qualitatively distinct predictions from many simple suboptimal rules. We find that all simple rules tested fail to describe human behavior, that the optimal rule accounts well for the data, and that several complex suboptimal rules are indistinguishable from the optimal one. Moreover, we found evidence that the optimal model is close to the true model: First, the better the trial-to-trial predictions of a suboptimal model agree with those of the optimal model, the better that suboptimal model fits; second, our estimate of the Kullback- Leibler divergence between the optimal model and the true model is not significantly different from zero. When observers receive no feedback, the optimal model still describes behavior best, suggesting that sensory uncertainty is implicitly represented and taken into account. Beyond the task and models studied here, our results have implications for best practices of model comparison.