Posterior Probability Matching and Human Perceptual Decision Making

Probability matching is a classic theory of decision making that was first developed in models of cognition. Posterior probability matching, a variant in which observers match their response probabilities to the posterior probability of each response being correct, is being used increasingly often in models of perception. However, little is known about whether posterior probability matching is consistent with the vast literature on vision and hearing that has developed within signal detection theory. Here we test posterior probability matching models using two tools from detection theory. First, we examine the models’ performance in a two-pass experiment, where each block of trials is presented twice, and we measure the proportion of times that the model gives the same response twice to repeated stimuli. We show that at low performance levels, posterior probability matching models give highly inconsistent responses across repeated presentations of identical trials. We find that practised human observers are more consistent across repeated trials than these models predict, and we find some evidence that less practised observers more consistent as well. Second, we compare the performance of posterior probability matching models on a discrimination task to the performance of a theoretical ideal observer that achieves the best possible performance. We find that posterior probability matching is very inefficient at low-to-moderate performance levels, and that human observers can be more efficient than is ever possible according to posterior probability matching models. These findings support classic signal detection models, and rule out a broad class of posterior probability matching models for expert performance on perceptual tasks that range in complexity from contrast discrimination to symmetry detection. However, our findings leave open the possibility that inexperienced observers may show posterior probability matching behaviour, and our methods provide new tools for testing for such a strategy.Author Summary: Decision making is partly random: a person can make different decisions at different times based on the same information. The theory of probability matching says that one reason for this randomness is that people usually choose the response that they think is most likely to be correct, but they sometimes intentionally choose the response that they think is less likely to be correct. Probability matching is a theory that was developed to describe how people try to predict the outcome of a partly random event, e.g., whether a patient has some medical condition, given the result of a medical test that does not provide perfectly accurate information. Recently, modified probability matching theories have been used to understand perceptual decision making, e.g., judging whether a sound and a visual flash were produced by the same event or by different events. We show that probability matching predicts that peoples’ perceptual decisions on difficult tasks are highly random and make poor use of the available information. We show experimentally that expert perceptual decisions are less random and more efficient than probability matching predicts. These findings help us understand how people perform a wide range of important real-world perceptual tasks, such as evaluating medical images and detecting targets in airport screening scans.