AI Insight
Humans consistently distort probability perception in a characteristic inverse-S pattern, overweighting small probabilities and underweighting large ones. This study proposes a Bayesian encoding-decoding framework in which internal probability representations are noisy and decoded via Bayes-risk minimization, decomposing distortion into boundary regression, likelihood repulsion, and prior attraction. The framework predicts and empirically recovers a U-shaped encoding precision profile, with greater sensitivity near 0 and 1, outperforming competing models across multiple experimental paradigms including frequency judgment, lottery pricing, and risky choice.
Why it matters
Understanding the mechanistic origin of probability distortion has direct implications for behavioral economics, risk communication, and the design of decision-support systems, as it reframes a longstanding cognitive bias as the product of rational inference under constrained neural encoding rather than an irrational quirk.
arXiv:2510.04698v3 Announce Type: replace
Abstract: Humans systematically misrepresent probability in a stereotyped inverse-S pattern. It has been documented for decades, but its origin remains unexplained. We propose a Bayesian encoding-decoding account in which probabilities are represented by noisy internal signals and decoded by Bayes-risk minimization. For bounded probability stimuli, we show that distortion decomposes into boundary regression, likelihood repulsion, and prior attraction, yielding a key prediction: the classic inverse-S-shaped weighting pattern implies a U-shaped allocation of encoding precision with greater sensitivity near 0 and 1. Across judgment of relative frequency, lottery pricing, and risky choice, this U-shape is recovered from data without imposing any functional form on the encoding, and our framework outperforms deterministic weighting functions, bounded log-odds models, uniform-encoding Bayesian accounts, and matched efficient-coding models on held-out data. In a new dot probability estimation experiment with bimodal stimulus statistics, the recovered prior tracks the new distribution while the recovered encoding remains U-shaped. Together, these results identify the inverse-S-shaped probability weighting function as the joint product of a stable U-shaped encoding and a flexible prior, integrated by optimal Bayesian decoding.
Source: The Bayesian Origin of the Probability Weighting Function in Human Representation of Probabilities