Probability weighting arises from boundary repulsions of cognitive noise

In both risky choice and perception, people overweight small and underweight large probabilities. While prospect theory models this with a probability weighting function, and Bayesian noisy coding models attribute it to specific encoding functions or priors, we propose a more general account: Probability distortions arise from cognitive noise being repelled by the natural boundaries of probability (0,1). This boundary repulsion occurs in any encoding-decoding system that efficiently encodes, or Bayesian-decodes, bounded quantities, independent of specific priors or encoding functions. Our theory predicts: new, experimentally-induced boundaries should cause additional distortions; increasing cognitive noise should amplify distortions; and boundaries should reduce behavioral variability near them. We confirmed all predictions in three pre-registered experiments spanning risky choice and probability perception. Our findings further suggest that these changes originate largely during decoding. Our work provides a unified explanation for distorted and variable probability judgments, reframing them as consequences of bounded, noisy cognitive inference.