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This paper theoretically and empirically investigates the role of 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 generate predictions about the relationships between subjective confidence, central tendency, and response variability. Specifically, our model clarifies that lower subjective confidence as a measure of posterior uncertainty about a j