{"ID":2859819,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.04698","arxiv_id":"2510.04698","title":"The Bayesian Origin of the Probability Weighting Function in Human Representation of Probabilities","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.04698","url_pdf":"https://arxiv.org/pdf/2510.04698v3","authors":"[\"Xin Tong\",\"Thi Thu Uyen Hoang\",\"Xue-Xin Wei\",\"Michael Hahn\"]","published":"2025-10-06T11:10:55Z","proceeding":"q-bio.NC","tasks":"[\"q-bio.NC\",\"cs.AI\",\"econ.TH\"]","methods":"[]","has_code":false}