Sample size dependence of Occam's razor in human decision-making

Abstract

To make sense of a noisy world, living beings constantly face decisions between competing interpretations for ambiguous sensory data. This process parallels statistical model selection, where most frameworks, like the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), are based on a trade-off between a models goodness-of-fit and its complexity and prescribe a bias towards simpler models (explanations). This same bias towards simplicity is generally reflected in human behavior. However, a core tenet of normative frameworks is that the trade-off should depend on the sample size (N): as more data becomes available, the goodness-of-fit grows faster than the "cost" of complex models, weakening the overall bias towards simplicity. It is unknown whether humans also conform to an analogous scaling principle, and if so, whether this behavior arises from an internal computation similar to that leading to the normative solution or from a simpler heuristic. Here, we investigate these questions using a preregistered visual task where participants inferred the number of latent Gaussian sources generating clusters of data-points, and where the number of points (N) presented on each trial is varied systematically. We consider three kinds of descriptions for participant behavior: one arising from a linear scaling of the weight of sensory evidence in N (as in BIC and AIC), one with no scaling, and one with sublinear scaling inspired by known biases in numerosity perception. Our results show that the normative, linear scaling description provides the worst account of human behavior. Instead, we find strong evidence for a sublinear scaling of effective sample size. By inferring the shape of this scaling with Gaussian Processes, we reveal two distinct scaling regimes for different ranges of N, consistent with numerosity perception biases. Our findings suggest that, when selecting between competing explanations for sensory data, humans employ an efficient heuristic that repurposes lower-level perceptual mechanisms to dynamically weight evidence against model complexity.