Counterfactual Reasoning Underlies the Learning of Priors in Decision Making

In everyday life, many people believe that two heads are better than one. Our ability to solve problems together appears to be fundamental to the current dominance and future survival of the human species. But are two heads really better than one? We addressed this question in the context of a collective low-level perceptual decision-making task. For two observers of nearly equal visual sensitivity, two heads were definitely better than one, provided they were given the opportunity to communicate freely, even in the absence of any feedback about decision outcomes. But for observers with very different visual sensitivities, two heads were actually worse than the better one. These seemingly discrepant patterns of group behavior can be explained by a model in which two heads are Bayes optimal under the assumption that individuals accurately communicate their level of confidence on every trial.

Decision-making behavior has been studied extensively, but the neurophysiological mechanisms responsible for this remarkable cognitive ability are just beginning to be understood. Here we propose neural computations that can account for the formation of categorical decisions about sensory stimuli by accumulating information over time into a single quantity: the logarithm of the likelihood ratio favoring one alternative over another. We also review electrophysio-logical studies that have identified brain structures that may be involved in computing this sort of decision variable. The ideas presented constitute a framework for understanding how and where perceptual decisions are formed in the brain.

Maintaining appropriate beliefs about variables needed for effective decision making can be difficult in a dynamic environment. One key issue is the amount of influence that unexpected outcomes should have on existing beliefs. In general, outcomes that are unexpected because of a fundamental change in the environment should carry more influence than outcomes that are unexpected because of persistent environmental stochasticity. Here we use a novel task to characterize how well human subjects follow these principles under a range of conditions. We show that the influence of an outcome depends on both the error made in predicting that outcome and the number of similar outcomes experienced previously. We also show that the exact nature of these tendencies varies considerably across subjects. Finally, we show that these patterns of behavior are consistent with a computationally simple reduction of an ideal-observer model. The model adjusts the influence of newly experienced outcomes according to ongoing estimates of uncertainty and the probability of a fundamental change in the process by which outcomes are generated. A prior that quantifies the expected frequency of such environmental changes accounts for individual variability, including a positive relationship between subjective certainty and the degree to which new information influences existing beliefs. The results suggest that the brain adaptively regulates the influence of decision outcomes on existing beliefs using straightforward updating rules that take into account both recent outcomes and prior expectations about higher-order environmental structure.