The Bayesian Origin of the Probability Weighting Function in Human Representation of Probabilities

Xin Tong, Thi Thu Uyen Hoang, Xue-Xin Wei and Michael Hahn

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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.

Date: 2025-10, Revised 2026-05
New Economics Papers: this item is included in nep-dcm, nep-evo and nep-upt
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