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. SignificanceThe origin of probability weighting--a central feature of decision-making under risk--remains a longstanding puzzle. Does it arise from processes unique to risk, or does it reflect a more general cognitive mechanism? Here, we show that the classic probability weighting pattern is not domain-specific but instead emerges from a general property of noisy inference over bounded quantities, such as probabilities. Our account formalizes how resource-rational encoding and Bayesian optimal decoding naturally lead to interactions between cognitive noise and the 0-1 bounds of probability, giving rise to systematic distortions. Using pre-registered experimental manipulations across both risky lottery valuation and probability perception, we demonstrate that distortions in probability weighting and estimation are not fixed, intrinsic features, but rather predictable consequences of the interaction between noise and boundaries. This provides a mechanistic account of probability weighting and suggests a unifying explanation for its emergence across different cognitive domains. Similar mechanisms should extend to other naturally or contextually bounded quantities.