Bayesian Signatures of Confidence and Central Tendency in Perceptual Judgment

This paper theoretically and empirically investigates the role of Bayesian noisy cognition in perceptual judgment, focusing on the central tendency effect: the well-known empirical regularity that perceptual judgments are biased towards the center of the stimulus distribution. Based on a formal Bayesian framework, we show that measures of subjective confidence can be used to explain the central tendency effects and response variability through a Bayesian lens. Specifically, our model clarifies that lower subjective confidence as a measure of posterior uncertainty about a judgment should predict (i) a lower sensitivity of magnitude estimates to objective stimuli; (ii) a higher sensitivity to the mean of the stimulus distribution; (iii) a stronger central tendency effect at higher stimulus magnitudes; and (iv) higher response variability. To test these predictions, we collect a tailored large-scale experimental data set and additionally re-analyze perceptual judgment data from several previous experiments. Across data sets, subjective confidence is strongly predictive of the central tendency effect and response variability, both correlationally and when we exogenously manipulate the magnitude of sensory noise. Our results lend support to Bayesian explanations of both confidence and the central tendency effect.